Transcript Document

SOUND WAVES
Sound is a longitudinal wave produced by a vibration that
travels away from the source through solids, liquids, or gases,
but not through a vacuum. The speed of sound is independent
of the pressure, frequency, and wavelength of the sound.
However, the speed of sound in a gas is proportional to the
temperature T. The following equation is useful in determining
the speed of sound in air
v = 331 + 0.6 T
Units: m/s
Where 331 is the speed of sound in m/s at 0°C, and T is
the temperature in °C
The speed of sound is different in different materials. The
speed of sound in air at room temperature (20ºC) is 343 m/s.
There are two main characteristic of sound: pitch and loudness.
Pitch refers to how high the sound is. It is measured by the
frequency. The higher the frequency the higher the pitch. The
lower the frequency the lower the pitch.
We hear frequencies in the range of 20 Hz to 20,000 Hz.
This is called the audible range.
Frequencies above this range are called ultrasonic.
Sound waves whose frequency is lower than the audible range
are called infrasonic.
HUMAN EAR:
The ear consists of three basic parts:
Outer ear: serves to collect and channel
sound to the middle ear.
Middle ear: serves to transform the
energy of a sound wave into the
internal vibrations of the bone
structure of the middle ear and
transform these vibrations into a
compressional wave in the inner ear.
Inner ear: serves to transform the energy of a compressional
wave within the inner ear fluid into nerve impulses which can
be transmitted to the brain.
Hearing:
A compression forces the eardrum inward and a rarefaction
forces the eardrum outward, thus vibrating the eardrum at the
same frequency of the sound wave.
SOURCES OF SOUND
Sound comes from a vibrating object. If an object vibrates with
frequency and intensity within the audible range, it produces
sound we can hear.
MUSICAL INSTRUMENTS
- String Instruments: guitar,
violin and piano
-Wind Instruments:
Open Pipe: flute and some
organ pipes
Closed Pipe: clarinet, oboe
and saxophone
STRING INSTRUMENTS
The sounds produced by vibrating strings are not very loud.
Many stringed instruments make use of a sounding board or
box, sometimes called a resonator, to amplify the sounds
produced. The strings on a piano are attached to a sounding
board while for guitar strings a sound box is used. When the
string is plucked and begins to vibrate, the sounding board or
box begins to vibrate as well. Since the board or box has a
greater area in contact with the air, it tends to amplify the
sounds.
On a guitar or a violin, the length of the
strings are the same, but their mass per
length is different. That changes the
velocity and so the frequency changes.
Standing waves are produced and the source vibrates in its
natural frequencies. The source is in contact with some
medium that allows the vibration to propagate.
WIND INSTRUMENTS
Wind instruments produce sound from the vibrations of
standing waves in columns of air inside a pipe or a tube.
In a string, the ends are nodes. In air columns the ends can be
either nodes or antinodes.
Open tube
Half Closed Tube
HARMONICS
a) For open pipe
The overtones will be multiples of the fundamental
b) For closed pipe
The overtones will be the odd multiples of the fundamental
INTERFERENCE OF SOUND WAVES: BEATS
If two sources are close in frequency, the sound from them
interferes and what we hear is an alternating sound level. The
level rise and falls. If the alternating sound is regular, it is
called beats.
The beat frequency equals the difference in frequencies
between the sources.
This is a way to tune musical instruments. Compare a tuning
fork to a note and tune until the beats disappear.
CI
Constructive
Interference
DI
Destructive
Interference
12.1 A saxophone plays a tune in the key of B-flat. The saxophone has a
third harmonic frequency of 466.2 Hz when the speed of sound in air is
331 m/s. What is the length of the pipe that makes up the saxophone?
n=3
f3 = 466.2 Hz
v = 331 m/s
f' = f3/n
= 466.2/3
= 233.1 Hz
Saxophone is closed so: L= 1/4 λ
1
1 v
331
L   

= 0.53 m
4(155.4)
4
4 f
12.2 An organ pipe that is open at both ends has a fundamental frequency
of 370.0 Hz when the speed of sound in air is 331 m/s. What is the length of
this pipe?
f' = 370 Hz
v = 331 m/s
L= 1/2 λ and v = λ f
v
331
L

= 0.447 m
2 f 2(370)
12.3 What is the fundamental frequency of a viola string that is 35.0 cm
long when the speed of waves on this string is 346 m/s?
L = 0.35 m
v = 346 m/s
L= 1/2 λ and λ = 2L
v
346
= 494.2 Hz

f  
 2 L 2(0.35)
v
12.4 A pipe that is open at both ends has a fundamental frequency of 125
Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe?
f' = 125 Hz
L = 1.32 m
L= 1/2 λ and λ = 2L
v=λf
=2 L f
= 2(1.32)(125)
= 330 m/s
12.5 A pipe that is closed on one end has a seventh harmonic frequency of
466.2 Hz. If the pipe is 1.53 m long, what is the speed of the waves in the
pipe?
n=7
f7 = 466.2 Hz
L = 1.53 m
L= 7/4 λ and λ = 4/7 L
 4L 
 41(1.53) 
v f 
  466.2  7  = 407.6 Hz


 7 
DOPPLER EFFECT
When a source of sound waves and a listener approach one
another, the pitch of the sound is increased as compared to the
frequency heard if they remain at rest. If the source and the
listener recede from one another, the frequency is decreased.
This phenomenon is known as the Doppler effect.
DOPPLER EFFECT:
The pitch heard by the listener is given by the following
equation:
v  vo
f '  fS
v  vS
Units: Hz
f' is the frequency of the sound heard by the listener
(observer),
fS is the frequency of the sound emitted by the source,
v is the speed of sound in air,
vS is the velocity of the source, and
vo is the velocity of the listener (observer).
Sign Convention:
(+) for approaching velocities and
(-) for receding velocities.
Light waves also exhibit the Doppler
effect. The spectra of stars that are
receding from us is shifted toward the
longer wavelengths of light. This is
known as the red shift.
Measurement of the red shift allows
astrophysicists to calculate the speed at
which stars are moving away. Since
almost all stars and galaxies exhibit a
red shift, it is believed that the universe
is expanding.
SHOCK WAVES AND THE SONIC BOOM
When the speed of a source of sound exceeds the speed of
sound, the sound waves in front of the source tend to overlap
and constructively interfere. The superposition of the waves
produce an extremely large amplitude wave called a shock
wave.
The shock wave contains a great
deal of energy. When the shock
wave passes a listener, this energy
is heard as a sonic boom.
The sonic boom is heard only for
a fraction of a second; however, it
sounds as if an explosion has
occurred and can cause damage.
12.6 A train whistle emits sound at a frequency of 400 Hz on a day when
the speed is 340 m/s.
a. What is the pitch of the sound heard when the train is moving toward a
stationary observer at a speed of 20 m/s?
v = 340 m/s
fS =400 Hz
vS = 20 m/s
 v  vo
f '  fs 
 v  vS

 340  0 

400


 = 425 Hz
 340  20 

b. What is the pitch heard when the train is moving away from the
observer at this speed?
 340  0 
f  400 
 = 377.78 Hz
 340  20 
'
vS = - 20 m/s
12.7 A stationary source of sound has a frequency of 800 Hz on a day when
the speed of sound is 340 m/s. What pitch is heard by a person who is
moving from the source at 30 m/s?
v = 340 m/s
fS = 800 Hz
vO = - 30 m/s
 v  vo
f '  fs 
 v  vS

 340  30  = 729.4 Hz

800



340


