Slide 1

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 2

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 3

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 4

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 5

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 6

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 7

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 8

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 9

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 10

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 11

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 12

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 13

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 14

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 15

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 16

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 17

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 18

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 19

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 20

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 21

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 22

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 23

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 24

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 25

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 26

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 27

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 28

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 29

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 30

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 31

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 32

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 33

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 34

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 35

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 36

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 37

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 38

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 39

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 40

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 41

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 42

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 43

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 44

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 45

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

►
►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
►
►

►
►
►
►

Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

►
►
►

Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5


Slide 46

WAVES

What is a wave?
►

A wave is a disturbance that passes through a medium. A wave
transmits energy not matter!

What is Sound?
►
►
►
►

sound is a type of wave
waves are caused by vibrations.
vibrations are the source of all sound.
a vibration is a repeated motion.

Classifying Waves
►

Electromagnetic Wave: is a wave which is capable of
transmitting its energy through a vacuum (i.e., empty space).
Electromagnetic waves are produced by the vibration of electrons
within atoms on the Sun's surface. These waves subsequently
travel through the vacuum of outer space, subsequently reaching
Earth.

►

Mechanical Wave: is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another. A sound wave is an example of a mechanical
wave.

Transverse Wave
►

Transverse Waves – are due to vibrations in which particles of
the medium move in a direction perpendicular to the direction
motion. ex. whip.

Longitudinal Waves
►

Longitudinal Waves – are due to vibrations in which particles of
the medium move in a direction parallel to the direction of
motion.

Properties of Transverse Waves
►
►

►
►

Crest: the highest point on a wave.
Trough: the lowest point on a wave.

Amplitude (A): the distance from the rest position to the
maximum displacement.
Wavelength (): the distance that one complete cycle of a wave
takes.

Properties of Longitudinal Waves

►
►
►

Compressions: regions where the particles come together
Rarefactions: regions where the particles are further apart.
Wavelength (): is the midpoint between successive
compressions and rarefactions.

Wave Terms
►

cycle: one complete repetition of the pattern or vibration.

►

period (T): the time required to complete one cycle.
T

t
# of cycles

►

Frequency ( f ): # of cycles per second. units: Hertz (Hz)
f

►

# of cycles
t

How does f relate to T?

f 

1
T

T

1
f

Phase
►

Waves in phase have crests and
troughs arriving at the same place
at the same time.

►

Waves out of phase have crests
that arrive coincident with a trough
of the second wave.

►

Objects are out of phase if during
any part of their cycles, the two
objects are moving in opposite
directions.

Practice Problems
►
►

PG 239 #1,2
PG 240 #3,4,5

Diffraction of Waves
►

When a straight wave propagates forward and passes through an
opening the wave tends to bend or diffract. Can also occur when
a wave passes an edge or around an object.

►

Diffraction helps us explain why we can hear around corners.

►

We tend to hear the lower bass notes more than the higher treble
notes when listening to music in another room due to the fact that
longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves
►

A wave can change it’s speed when it enters a new medium. It’s
frequency will remain the same. i.e. if there are 10 crests
approaching the boundary between the media then 10 crests
should enter the new medium.

►

The wavelength does change though. If the wave slows down the
waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
►

One dimensional waves react in a special way when
they are reflected.

►

In the case of a fixed-end reflection a crest reflects as
a trough and a trough reflects as a crest.

►

On the other hand if the reflection occurs from a freeend, where the medium or particles are free to move,
there is no inversion. Crests reflect as crests and
troughs reflect as troughs.

►

In both fixed and free end reflections there is no change
in wavelength, frequency or the speed of the pulse,
since the medium is the same.

►

When a waves travels through a different medium it’s
speed and wavelength change.

►

At the boundary between the 2 media, some reflection
occurs. It is called partial reflection.

►

The phase of transmitted waves is unaffected in all
partial reflections, but inversion of the reflected wave
occurs when the wave passes from a fast medium to a
slow medium.

Speed of Waves
►

The Universal Wave Equation

►

When we create a transverse wave with a rope we must perform
one complete vibration to have one complete wave.

►

The wave travels one complete wavelength (λ) in the time it
takes to complete one period of vibration (T).

►

We already know.

►

If we substitute λ for ∆d and
T for ∆t we get .

►

We can also express in terms
of frequency as well:

velocity 

v

d
t


T

v

1



T
v  f 

►

Practice

PG 248. #1,2
PG 250. #1,2,3,4
PG 251. #5,6,7

Speed of Sound
►
►

At normal atmospheric pressure and at 0° C, it is 331 m/s (about
1200km/h).
If the atmospheric pressure remains constant, the speed of sound
increases as the temperature increases. The speed changes by
0.6m/s for each degree Celsius.

Speed of Sound in Air  ( 331 0.6T ) m s
►

(At normal atmospheric pressures)
Facts: sound travels 15 times faster in steel than it does in air
sound travels 4 times faster in water than air
(pg 278 for more)

►

Practice

PG 277. #1,2
PG 279. #1,2,3
PG 280. #1,2,5,6

Mach Number
►

We use Mach number rather than kilometres per hour for high
speed aircraft like a Concorde jet.
Mach Number 

speed of object
speed of sound

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►

It is the ratio of the speed of the object to the speed of sound.
Therefore to travel Mach 1 you must travel the speed of sound
1200km/hr.
► Top 50 Fastest Aircraft

The Sound Barrier
►
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►

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Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the
wing. Compressions travel forward, faster than the wing.
As a result, compressions push other air molecules out of the
way.
Sonic or Supersonic Speeds: at the speed of sound or greater.
The compressions cannot move faster than the wing.
Air molecules pile up at the front of the wing.
Sometime a pile of air molecules would spill above or below the
wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom.
►

This spillage of air molecules about the wing causes a shock
wave to be produced.

►

This shock wave continuously spreads out from its source. When
you hear this boom it does not mean the sound barrier has just
been broken rather an object in the area is flying at or faster than
the speed of sound.

►

Other examples include: flapping of a flag, crack of a whip or a
wet towel.

Doppler Effect
►

Sound from a point source:

►

Sound from a moving point source:
Audio of a car horn.

►

►

Once the moving source reaches the speed of sound,
the wave fronts pile up on one another in the direction
of motion.

►

For any moving object the waves in the direction of
motion will have a smaller wavelength and higher
frequency.

►

The trailing waves have a larger wavelength and a
lower frequency.

►

Austrian mathematician and physicist, Christian
Doppler (1803-53) 1st noticed this effect hence the
name, “The Doppler Effect”

Interference
►

when two or more waves act simultaneously on the same
particles in a medium.

►

Principle of Superposition: The resultant displacement of a
given particle is equal to the sum of the displacements that would
have been produced by each individual wave acting
independently.

Constructive Interference
►

Constructive Interference: when the resultant displacement is
greater than the displacement that would be caused by either
wave by itself.

►

A crest that meets a crest produces a supercrest.
A trough that interferes with a trough produces a supertrough

►

Destructive Interference
►

Destructive Interference: when the resultant displacement is
smaller than the displacement that would be caused by one wave
itself.

Web
►

When positive and negative pulses of equal amplitude and shape,
traveling in opposite directions, interfere, there is a point that
remains at rest throughout the interference. This we call a node
or nodal point (N).
2 Speakers

Special Interference Patterns
►
►
►

Standing Waves
2 Point Source
Beat Frequency

*Standing Waves
►

In stationary, or standing waves, the shape, or profile of the
wave stays fixed in a medium. Ex. plucking the string of a string
instrument.

►

When the string is plucked, a wave is caused to travel up and
down it. Since both ends of the string are fixed, the waveform is
reflected back up and down the string, or its path, causing a wave
to stay constant within it.

►

A sound is produced because the energy within the string that is
used to create the standing wave is also creating a progressive
wave, the sound wave you hear.

Beat Frequency
►

Alternating constructive and destructive interference of sound
waves can be heard as a change in sound pattern from loud to
soft to loud, etc. These periodic changes in sound intensity are
called beats.

►

The maximum number of intensity points that occur per second
is called the beat frequency.

►

Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources)

►

Web1, Web2

►

When two sources have the same frequency that is f1 = f2 then no
beats are heard and we can say they are in tune.

►

As the beat frequency decreases when we adjust a source, as we
would when tuning a guitar, the frequencies of each source get
closer.

►

Practice

PG 282. #1,2
PG 284. #4,5

*Standing Waves
►

►

When we attach on end of a string to a stationary object and send
a wave down the string the wave will return. If the returning
wave is identical to the original wave a standing wave will be
produced.

each vibrating section is called a loop.
► loops alternate from being a supercrest to a supertrough
► it cannot be both at the same time and therefore represents half a
wavelength

Frequency and Wavelength
►

We know that 1 loop represents half a wavelength.

►

Therefore: λ1= 2L (L being the length of the string
containing 1 loop)
In terms of the universal wave equation:
f1 

►

v

1

f1 

v
2L

When 2 loops form in a string then λ2 = L. In wave equation
terms:
f2 

v
L

f 2  2 f1

►

This would mean that the second harmonic has twice the
frequency as the first harmonic. Also, the third harmonic has 3
x’s the frequency as the first.

►

Standing wave patterns are called harmonics only if their
frequencies are whole-number multiples of the first harmonic.

What is Pitch?
►

Pitch is a term that is often substituted for frequency in musical
references.

Standing wave patterns in a string.
Number of Loops

Scientific Name

Musical Name

1

first harmonic

fundamental

2

second harmonic

first overtone

3

third harmonic

second overtone

4

fourth harmonic

third overtone

►

Sound quality of a musical note depends on the number and
relative intensity of the overtones it produces, along with the
fundamental.

►

The pitch of a note being played on, say, a guitar depends on:
The length of the string.
The tension of the string.
The material the string is made of.

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►
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Resonance
►

The frequency or frequencies at which an object tends to vibrate
with when hit, struck, plucked, strummed or somehow disturbed
is known as the natural frequency of the object.

Ex. Pushing a friend on a swing.
►

When the frequency of forced vibrations on an object matches
the object's natural frequency, a dramatic increase in amplitude
occurs. This phenomenon is called resonance .
Ex. The rattling dash in a car.
Radio waves & antenna.
2 Tuning forks demo

►

When the resonance involves mechanical systems like
pendulums or springs, it is known as mechanical resonance.

►

Resonance can be destructive.
Tacoma Narrows, Washington State (1940). A 64km/h wind
matched the natural frequency of a suspension bridge. As time
passed the bridge began to resonate and within and hour was torn
apart in the middle.

►

A similar event happened to a pedestrian bridge in London,
England (2000)

Acoustical Resonance
►

When a resonance involves sound waves we call it acoustical
resonance.
Ex. Blowing over the mouth of an empty bottle.

►

Resonance can occur tube-like structures if a standing wave is
setup involving air molecules.

Closed Air Columns
►

A close end air column will produce a fixed end reflection and a
standing wave will result.

►

The bottom of the column will always be a nodal point.

►

If the length is such that the column ends in the middle of a loop,
the sound will be amplified.

Open Air Columns
►

An open column will produce a free end reflection causing a
standing wave to be produced.

►

The end of the column will always be a antinode and the sound
will be amplified.

► Practice

PG 302. #1,2
PG 303. #1,2
PG 305. #1,2
PG 306. #1,2,3,4,5