Transcript Introduction to Modern Physics PHYX 2710

Physics of Technology
PHYS 1800
Lecture 35
Introduction
Section 0
Waves
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 1
PHYSICS OF TOF
ECHNOLOGY
- PHYS 1800
PHYSICS
TECHNOLOGY
ASSIGNMENT SHEET
Spring 2009Spring
Assignment
Sheet
2009
Date
Day
Lecture
Feb 16
M
Presidents Day
17
Tu
Angular Momentum (Virtual Monday)
18
W
Review
19
H
Test 2
20
F*
Static Fluids, Pressure
Feb 23
M
Flotation
25
W
Fluids in Motion
27
F*
Temperature and Heat
Mar 2
M
First Law of Thermodynamics
4
W
Heat flow and Greenhouse Effect
6
F*
Climate Change
Mar 9-13
M-F
Spring Break
Mar 16
M
Heat Engines
18
W
Power and Refrigeration
20
F*
Electric Charge
Mar 23
M
Electric Fields and Electric Potential
25
W
Review
26
H
Test 3
27
F*
Electric Circuits
Mar 30
M
Magnetic Force Review
Apr 1
W
Electromagnets
3
F
Motors and Generators
Apr 6
M
Making Waves
8
W
Sound Waves
10
F*
E-M Waves, Light and Color
Apr 13
M
Mirrors and Reflections
Introduction
Section
0 Lecture 1 Slide 2
15
W
Refraction and Lenses
17
F*
Telescopes and Microscopes
Apr 20
M
Review
22
W
Seeing Atoms
24
F
The really BIG & the really small
INTRODUCTION TO Modern Physics PHYX 2710
May
1
F
Final Exam: 09:30-11:20am
Chapter
No Class
8
5-8
5-8
9
9
9
10
10
10
No Classes
11
11
12
12
13
9-12
13
14
9-12
14
15
15
16
17
17
17
1-17
18 (not on test)
21 (not on test)
Homework Due
-
6
7
8
-
9
10
11
No test week
12
Fall 2004
* = Homework Handout
*Homework Handout
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 2
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 3
Examples of Wave Phenomena
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 3
UNIT FOUR
Wave Motion and Optics
Introduction
Section 0
Lecture 1
Wave motion
describes
phenomena
ranging from
the
familiar...
Ocean
waves...
Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 4
Sound
waves...
Introduction
Section 0
Lecture 1
Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 5
Light
waves...
Introduction
Section 0
Lecture 1
... to the
less familiar
realm of
atomic
physics...
Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 6
...even
Quantum
Physics
(matter
waves)...
Introduction
Section 0
Lecture 1
Slide 7
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 7
Introduction
Section 0
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
... and Relativity
Lecture 1
Slide 8
(gravity waves).
Waves
Lecture 35 Slide 8
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 9
Review of Oscillations
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 9
Restoring Forces and Oscillations
• A restoring force is a force
that exerts a push or a pull
back towards equilibrium.
• A restoring force that increases
in direct proportion to the
distance from equilibrium
results in simple harmonic
motion.
Introduction
Section 0
Lecture 1
Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 10
Springs and Simple Harmonic Motion
• Simple harmonic motion occurs when the
energy of a system repeatedly changes from
potential energy to kinetic energy and back again.
Energy added by doing work
to stretch the spring is
transformed back and forth
between
potential
Introduction
Section 0energy
Lecture 1 Slide 11
and kinetic energy.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 11
Oscillatory Motion
The horizontal position x of the mass on the spring is plotted
against time as the mass moves back and forth.
• The period T is
the time taken for
one complete
cycle.
• The frequency f is
the number of
cycles per unit
time. F=1/T
• The amplitude is
the maximum
distance
from Section 0
Introduction
equilibrium.
Lecture 1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
X(t) = A sin (2π f t)
Waves
Lecture 35 Slide 12
Energy and Oscillations
Why does a
swinging
pendant
return to the
same point
after each
swing?
Introduction
Section 0
Lecture 1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 13
Energy and Oscillations
The force
does work
to move
the ball.
This
increases
the ball’s
energy,
affecting
its Introduction
motion.Section 0
Lecture 1
Slide 14
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 14
Compressionand Oscillation on an Atomic Scale
Bonds between atoms in a compressed solid can be treated as
compressed springs.
Section 0
Lecture 1
FSlide
=-k Δx
spring
15
+
+
+
Introduction
+
+
+
+
+
Ultimately the forces come from electrostatic interactions
between electrons and protons (and a little quantum mechanics).
+
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 15
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 16
Making Waves
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 16
What Are Waves?
Water seems to move toward the shore, but no water
accumulates on the beach.
What is actually
moving?
Introductioncarry
Section 0
Do the waves
energy?
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 17
A List of Types of Waves Waves?
System
Medium
Introduction
Amplitude and Units
Section 0
Lecture 1
Typical Frequency
Range
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 18
Wave Pulses and Periodic Waves
A Slinky is
ideal for
studying
simple
waves.
Introduction
Section 0
Lecture 1
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 19
Wave Pulses and Periodic Waves
• If a Slinky is laid out on a smooth table with one end held
motionless, you can easily produce a single traveling pulse:
– With the Slinky slightly stretched, move the free end back and
forth once along the axis of the Slinky.
– You will see a disturbance (the wave pulse) move from the free
end of the Slinky to the fixed end.
• What is actually moving?
– The pulse moves through the Slinky, and portions of the Slinky
move as the pulse passes through it.
– After the pulse dies out, the Slinky is exactly where it was before
the pulse began.
Introduction
Section 0
Lecture 1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 20
Wave Pulses and Periodic Waves
•
Moving one end of the Slinky back and forth created a local compression
where the rings of the spring are closer together than in the rest of the
Slinky.
– This region of compression moves along the Slinky and constitutes the pulse.
– The wave or pulse moves through the medium (here, the Slinky), but the medium
goes nowhere.
– What moves is a disturbance within the medium which may be a local
compression, a sideways displacement (like a wave on a rope), etc.
•
The speed of the pulse may depend on factors such as tension in the Slinky
and the mass of the Slinky.
Introduction
Section 0
Lecture 1
Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 21
Wave Pulses and Energy
• Energy is transferred through the Slinky as the pulse travels.
– The work done in moving one end of the Slinky increases both the
potential energy of the spring and the kinetic energy of individual
loops.
– This region of higher energy then moves along the Slinky and
reaches the opposite end.
– There, the energy could be used to ring a bell or perform other types
of work.
• Energy carried by water waves does substantial work over time
in eroding and shaping a shoreline.
Introduction
Section 0
Lecture 1
Slide 22
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 22
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 23
Transverse and Longitudinal Waves
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 23
Longitudinal Waves
• The pulse we have
been discussing is a
longitudinal wave: the
displacement or
disturbance in the
medium is parallel to
the direction of travel
of the wave or pulse.
• Sound waves are
longitudinal.
Introduction
Section 0
Lecture 1
Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 24
Transverse Waves
• By moving your hand up
and down, you could also
produce a transverse
wave, in which the
displacement or
disturbance is
perpendicular to the
direction the wave is
traveling.
• Waves on a rope and
electromagnetic waves
are transverse.
• Polarization effects are
associated with
transverse waves but
Section 0 Lecture 1 Slide
not Introduction
longitudinal
waves.
• Water waves have
both longitudinal and
transverse properties.
25
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 25
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 26
Longitudinal Waves on a Slinky
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 26
Generating Longitudinal Waves
• If instead of moving your hand back and forth just once, you
continue to produce pulses, you will send a series of
longitudinal pulses down the Slinky.
– If equal time intervals separate the pulses, you produce a periodic
wave.
– The time between pulses is the period T of the wave.
– The number of pulses or cycles per unit of time is the frequency f =
1/T.
– The distance between the same points on successive pulses is the
wavelength .
– A pulse travels a distance of one wavelength in a time of one
period.
– The speed is then the wavelength divided by the period:
Introduction
Section 0
Lecture 1
v
Slide 27

T
 f
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 27
Longitudinal Waves
A longitudinal wave traveling on a Slinky has a period of 0.25 s
and a wavelength of 30 cm. What is the frequency of the wave?
a)
b)
c)
d)
e)
0.25 Hz
0.30 Hz
0.83 Hz
1.2 Hz
4 Hz
T  0.25 s
1
1
f  
 4 Hz
T 0.25 s

Introduction
Section 0
Lecture 1
Slide 28
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 28
Longitudinal Waves
A longitudinal wave traveling on a Slinky has a period of 0.25 s and
a wavelength of 30 cm. What is the speed of the wave?
a)
b)
c)
d)
e)
0.25 cm/s
0.30 cm/s
1 cm/s
7.5 cm/s
120 cm/s
v f
 4 Hz30 cm
 120 cm/s

Introduction
Section 0
Lecture 1
Slide 29
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 29
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 30
Transverse Waves on a String
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 30
Generating A Transverse Pulse
• A snapshot of a single transverse pulse moving along a rope is
like a graph of the vertical displacement of the rope plotted
against the horizontal position.
• At some later
time the pulse will
be farther down
the rope at a
different
horizontal
position.
Introduction Section 0
• The shape
remains basically
the same.
Lecture 1
Slide 31
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 31
Generating A Transverse Wave
• If you repeat a series of identical pulses at regular time intervals, you
might produce a periodic wave such as shown.
– The wavelength  is the distance covered by one complete cycle of the
wave.
– This wave pattern moves to the right along the rope, retaining its shape.
– The shape depends on the exact motion of the hand or other oscillator
generating the wave.
• When the leading edge of the wave reaches the fixed end of the rope,
it will be reflected and start to move back to the left.
– The reflected wave will interfere with the wave still traveling to the right.
Introduction
Section 0
Lecture 1
Slide 32
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 32
Generating A n Harmonic Wave
• If you move your hand up and down smoothly in simple harmonic
motion, the displacement of this end of the rope will vary
sinusoidally with time.
– The resulting periodic wave will also have a sinusoidal form.
– Such a wave is called a harmonic wave.
– The individual segments of rope tend to move with simple harmonic
motion, because the restoring force pulling the rope back toward the
center line is proportional to its distance from the center line.
• Any periodic wave can be represented as a sum of harmonic waves
with different wavelengths and frequencies.
– The process of breaking a complex wave down into its simple harmonic
components is called Fourier, or harmonic analysis.
Introduction
Section 0
Lecture 1
Slide 33
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 33
Wavelength
A wave on a rope is shown below. What is the
wavelength of this wave?
a) 1/6 m
b) 1 m
Introduction
Section 0
Lecture 1
c) 2 m
d) 3 m
e) 6 m
Slide 34
In 6 m, the wave goes through 2 complete cycles.
The wavelength (length of one complete cycle) is (6 m)/2 = 3 m.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 34
Frequency of a Wave
If the frequency of the wave is 2 Hz, what is
the wave speed?
a) 1/6 m/s
b) 2/3 m/s
Introduction
c) 2 m/s
v  f  2 s
Section 0
Lecture 1
d) 3 m/s
e) 6 m/s
3 m  6 m/s
Slide-135
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 35
Frequency of a Wave
• As the raised portion of a pulse approaches a given point on the
rope, the tension in the rope acquires an upward component.
– The resulting upward force
causes this next segment
to accelerate upward, and
so on down the rope.
• The speed of the pulse
depends on how fast
succeeding segments can be
started moving (accelerated).
• By Newton’s second law, this is proportional to the force and
a
inversely proportional to the mass of the segment:
• A larger tension produces a larger acceleration.
F
• The speed of the pulse will increase with the
v
Section 0 Lecture 1 Slide 36
tensionIntroduction
and decrease
with the mass per unit

length of the rope:
 where   m
L
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
F
m
Waves
Lecture 35 Slide 36
Velocity of a Wave
A rope has an overall length of 10 m and a total mass of 2 kg. The
rope is stretched with a tension of 50 N. One end of the rope is
fixed, and the other is moved up and down with a frequency of 4 Hz.
What is the speed of waves on this rope?
a) 5.0 m/s b) 7.07 m/s c) 15.8 m/s d) 50 m/s e) 250 m/s
m 2 kg
 
 0.2 kg/m
L 10 m
Introduction Section 0 Lecture 1 Slide 37
F
50 N
=

 250 m2 /s2  15.8 m/s

0.2 kg/m
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 37
Wavelength of a Wave
A rope has an overall length of 10 m and a total mass of 2 kg.
The rope is stretched with a tension of
50 N. One end of the rope is fixed, and the other is moved
up and down with a frequency of 4 Hz.
What is the wavelength?
a) 0.20 m
b) 3.95 m
c) 10 m
d) 15.8 m
e) 25 m/s
 f
Introduction
Section 0
Lecture 1

INTRODUCTION TO Modern Physics PHYX 2710
Slide 38
v 15.8 m/s

 3.95 m
f
4 Hz
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 38
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 39
Interference and Standing Waves
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 39
Interference and Standing Waves
• When a wave on a rope reaches the fixed end of the
rope, it is reflected and travels in the opposite
direction back toward your hand.
– If the wave is periodic, the reflected wave interferes with the
incoming wave.
– The resulting pattern becomes more complex and confusing.
– This process, in which two or more waves combine, is called
interference.
Introduction
Section 0
Lecture 1
Slide 40
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 40
Superposition
• Imagine a rope consisting of two identical segments spliced together
to form a single rope of the same mass per unit length as the two
original segments.
– Identical waves traveling on
the two identical segments
will combine to form a larger
wave on the single joined
rope.
– At all points, the height of the
individual waves will add
together to form a wave with
the same frequency and
wavelength but twice the
height of the initial two waves.
Introduction Section 0 Lecture 1 Slide 41
Principle
of Superposition:
When two or more waves combine, the resulting
disturbance or displacement is equal to the sum of the
individual disturbances.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 41
Interference
• When the two waves are moving the same way at the same time, they
are in phase.
– The resulting combined wave will be larger (have a greater height).
• If one wave is moving
upward when the other
wave is moving downward,
the two waves are
completely out of phase.
– If the two waves have the
same height, the resulting
combined displacement will
be zero.
– No wave is propagated beyond the junction.
• The result of adding two waves together depends on their phases as
well as on their height or amplitude.
• When waves are in phase, we have constructive interference.
Introduction Section 0 Lecture 1 Slide 42
• When waves are out of phase, we have destructive interference.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 42
Interference
• When two or more waves are traveling in the same direction, the
difference in phase determines whether the interference will be
constructive, destructive, or somewhere in between.
• When two waves are traveling in opposite directions, such as when a
wave is reflected back on itself, the principle of superposition can be
applied at different points on the string.
– At point A, the two waves cancel each other at all times.
– At this point, the string will not oscillate at all; this is called a node.
At point B, both waves
will be in phase at all
times.
• The two waves always
add, producing a
Introduction
Section
0 of
Lecture
displacement
twice
that
each wave by itself.
• This is called an
antinode.
•
1
Slide 43
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 43
Standing Waves
• This pattern of oscillation is called a standing wave.
– The waves traveling in opposite directions interfere in a way that
produces a standing or fixed pattern.
– The distance between adjacent nodes or adjacent antinodes is half the
wavelength of the original waves.
– At the antinodes, the string is oscillating with a large amplitude.
– At the nodes, it is
not moving at all.
– At points between
the nodes and
antinodes, the
amplitude has
intermediate
values.
Introduction
Section 0
Lecture 1
Slide 44
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 44
Pitch
• Guitars, pianos, and other stringed instruments produce
music using standing waves on strings.
– The frequency of the sound wave equals the string’s frequency of
oscillation and is related to the musical pitch.
– A higher frequency represents a higher-pitched sound.
Introduction
Section 0
Lecture 1
Slide 45
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 45
Harmonics
• For a string fixed at both ends, the simplest standing wave, the
fundamental or first harmonic, has nodes at both ends and an
antinode in the middle.
The wavelength is determined by
the length of the string.
• Since the distance between
nodes is half the wavelength, the
wavelength must be twice the
length of the string.
• The wave speed is determined by
the tension in the string and the
mass per unit length of the string.
• The frequency can then be found
using the relationship v = f :
•
Introduction
Section 0
Lecture 1
Slide 46
v
v
f  
 2L
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 46
Octaves
• A string with a longer length L will result in a lower frequency.
– The effective length can also be shortened by placing your finger firmly
on the string,
producing a higher-pitched
tone.
• Other patterns of oscillation
may also be produced.
•The
second harmonic has a
node at the midpoint of the
string, and a wavelength equal
to L.
•This wavelength is half the
fundamental, so its frequency
Introduction Section 0 Lecture 1 Slide
is twice
the fundamental.
•Musically, this pitch would be
an octave above the
fundamental.
47
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 47
• A string with a longer length L will result a lower frequency.
– The effective length can also be shortened by placing your finger firmly
on the string,
producing a higher-pitched
tone.
• Other patterns of oscillation
may also be produced.
The
third harmonic has four nodes
(counting the ones at the ends) and
three antinodes, and a wavelength
equal to two-thirds L.
The resulting frequency is three
times the fundamental and 3/2 that
Introduction Section 0 Lecture 1 Slide 48
of the second
harmonic.
Musically, this is called a fifth
above the second harmonic.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 48
A guitar string has a mass of 4 g, a length of 74 cm, and a
tension of 400 N. These values produce a wave speed of 274
m/s. What is its fundamental frequency?
a)
b)
c)
d)
e)
1.85 Hz
3.70 Hz
185 Hz
274 Hz
370 Hz
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 49
L  74 cm  0.74 m
v  274 m/s
  2L
v
v
f1  
1 2L
274 m/s

1.48 m
 185 Hz
Waves
Lecture 35 Slide 49
A guitar string has a mass of 4 g, a length of 74 cm, and a
tension of 400 N. These values produce a wave speed of 274
m/s. What is the frequency of the second harmonic?
a)
b)
c)
d)
e)
92.5 Hz
123 Hz
185 Hz
370 Hz
740 Hz
Introduction Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 50
L  74 cm  0.74 m
v  274 m/s
L
v v
f2 

2 L
274 m/s

0.74 m
 370 Hz
Waves
Lecture 35 Slide 50
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 51
Sound Waves
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 51
Sound Waves
• Sound waves may be generated in many ways in addition to
an oscillating string.
• Since sound waves reach our ears, they must be able to
travel through air.
The bass
string has
been
plucked,
producing a
blur near
the middle
where theIntroduction
amplitude is
greatest.
Section 0
Lecture 1
Slide 52
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 52
Sound Waves
• A sound wave consists of pressure variations in air.
– The diaphragm of a speaker oscillates back and forth, producing regions
of higher pressure and lower pressure.
– These regions propagate through the air as variations in air pressure and
density, forming a longitudinal sound wave.
Introduction
Section 0
Lecture 1
Slide 53
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 53
Sound Waves
• We can show these pressure variations in a graph of pressure
plotted against position.
• The factors that determine the speed of sound are related to how
rapidly one air molecule transmits changes in velocity to nearby
molecules to propagate the wave.
– In room temperature air, sound
waves travel with a speed of
340 m/s or 750 MPH.
– For gases other than air, the
speed also depends on the
masses of the molecules or
atoms.
– Sound waves can also travel
through liquids and solids, often
with higher speeds.
Introduction
Section 0
Lecture 1
Slide 54
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 54
Sound Waves
• Interference phenomena such as standing waves can be observed in
sound waves.
– Many musical instruments produce standing waves in a tube or pipe.
– If the tube is closed at one end, such as a bottle, there is a displacement
node at the closed end.
– At the open end, there is a displacement antinode.
• The frequency of the standing
wave can be found from the
speed of sound in air and the
wavelength:
f 
v


340 m/s

where the wavelength is
determined
by Section
the length
Introduction
0 Lectureof
1
the tube.
Slide 55
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 55
• The standing-wave patterns for the first three harmonics for a tube
open at one end and closed at the other are represented as follows:
The first harmonic or
fundamental has a wavelength
four times longer than the length
of the tube.
• The wavelength of the second
harmonic is equal to four-thirds of
the length of the tube.
• The wavelength of the third
harmonic is equal to four-fifths of
the length of the tube.
• etc.
•
Introduction
f 
v

Section 0

Lecture 1
Slide 56
340 m/s

INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 56
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 57
Doppler Effect
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 57
The Doppler Effect
• A moving source of sound, such as a car horn, seems to change pitch
depending on its motion relative to the listener.
• As a car passes a
stationary observer, the
horn’s pitch changes
from a higher pitch to a
lower pitch.
Introduction Section 0 Lecture
1
Slide 58
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 58
The Doppler Effect
• Comparing the wavefronts for a stationary car horn and for a moving
car horn illustrates why the pitch changes.
• When the car is
approaching the
observer, the
wavefronts reaching
the observer are closer
together.
• When the car is
moving away from the
observer,
the Section 0 Lecture
Introduction
wavefronts reaching
the observer are farther
apart.
1
Slide 59
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 59
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 60
The Physics of Music
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 60
The Physics of Music
 Why do certain combinations of notes (chords) sound
better than others?
 Musical notes actually have a mix of higher harmonics along
with the fundamental frequency.
 The relationships between these different frequencies explain
why some notes sound harmonious together, and others do
not.
 An analysis of the mixture of frequencies is called harmonic or
frequency analysis.
Introduction
Section 0
Lecture 1
Slide 61
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 61
• When a guitar string is plucked in the usual position, the second
and third harmonics often dominate the harmonic spectrum.
– f1 is the frequency of the first harmonic.
– Since the string is usually plucked right where the second harmonic (f2
= 2f1) has an antinode, the second harmonic is strongly stimulated.
– The body of the guitar
also determines which
harmonics will be
reinforced.
Introduction
Section 0
Lecture 1
Slide 62
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 62
• When a guitar string is plucked near the bridge, many higher
harmonics are present in the harmonic spectrum.
– This results in a twangy sound.
– The pitch still sounds the same, but the tone quality depends on the
mixture of harmonics present.
• Different instruments generate different harmonic mixes, so they
have different
tones.
– A trumpet produces a
lot of higher harmonics
so it sounds “bright”
or “brassy”.
– A flute can produce a
tone dominated by the
fundamental frequency,
withIntroduction
almost none
of the
Section 0
Lecture
higher harmonics, so
the tone sounds “pure”.
1
Slide 63
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 63
• When discussing musical notes, we describe the difference in
frequencies in terms of musical intervals.
• Musical scales and intervals are based upon the ratios between
the higher harmonics in the notes.
– The frequency of the second harmonic is twice that of the first
harmonic. This interval is an octave, and corresponds to the interval
from one note C to the next higher C (the first and eighth notes in the
scale).
– The frequency of the third harmonic is 3/2 that of the second
harmonic. This interval is
a fifth, between the first
and fifth notes in the scale
(C and G).
– The frequency of the fourth
harmonic is 4/3 that of the
Section
0 Lecture 1
thirdIntroduction
harmonic.
This
interval is a fourth,
between the first and
fourth notes (C and F).
Slide 64
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 64
• Just tuning involves tuning an instrument so that in one key, all
the intervals have simple frequency ratios.
– In a different key, the tuning may not sound correct.
• Equally-tempered tuning is a compromise so that the ratios are all
approximately correct, but not perfect.
– The ratios between
adjacent half steps on
the scale are all identical,
so the scales sound
correct regardless of
what key you are in.
– The frequency of the fifth harmonic is 5/4 that of the fourth harmonic.
This interval is a major third, between the first and third notes (C and
E).
Introduction
Section 0
Lecture 1
Slide 65
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 65
A C-major scale begins with do on middle C having a
frequency of approximately 264 Hz. Assuming that they have
been tuned to the perfect ratios for the intervals in question,
what should the frequency be for sol (G)?
a)
b)
c)
d)
e)
88 Hz
132 Hz
176 Hz
396 Hz
528 Hz
sol is a fifth abovedo with a ratio of3 2 :
3
f  264 Hz  396 Hz
2

Introduction
Section 0
Lecture 1
Slide 66
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 66
A C-major scale begins with do on middle C having a
frequency of approximately 264 Hz. Assuming that they have
been tuned to the perfect ratios for the intervals in question,
what should the frequency be for fa (F)?
a)
b)
c)
d)
e)
fa is a fourth abovedo with a ratio of4 3 :
4
f  264 Hz  352 Hz
3
176 Hz
198 Hz
352 Hz
440 Hz
528 Hz 
Introduction
Section 0
Lecture 1
Slide 67
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 67
A C-major scale begins with do on middle C having a
frequency of approximately 264 Hz. Assuming that they have
been tuned to the perfect ratios for the intervals in question,
what should the frequency be for do at the top of the scale
(high C)?
a)
b)
c)
d)
e)
From do to the next higher
do is an octave,
which doubles the frequency:
88 Hz
198 Hz
352 Hz
440 Hz
528 Hz 
Introduction
f  2264 Hz  528 Hz
Section 0
Lecture 1
Slide 68
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 68
– Combinations of notes sound harmonious when the higher
harmonics overlap.
– When two notes are too close in pitch, beats can produce a
dissonant buzz.
– The two waves come in and out of phase as time progresses.
Introduction
Section 0
Lecture 1
Slide 69
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 69
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 70
Electric Waves (AC Current)
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 70
Alternating Current and Household Circuits
• The current we draw from a wall outlet is alternating current
(ac) rather than direct current (dc).
– Direct current implies that the current flows in a single
direction from the positive terminal of a battery or power
supply to the negative terminal
– Alternating current continually reverses its direction -- it flows
first in one direction, then in the other, then back again.
– In North America the ac goes through 60 cycles each second
(60 Hz).
Introduction
Section 0
Lecture 1
Slide 71
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 71
Alternating Current and Household Circuits
• The plot of electric current as a function of time for an
alternating current is a sinusoidal curve.
– The average value of an ordinary alternating current is zero.
– The power dissipated in a resistance is proportional to the
square of the current.
– The effective current or rms current is obtained by squaring
the current, averaging this value over time, and taking the
square root of the result.
– The effective current Ieff is 0.707 times the peak current Ipeak.
Introduction
Section 0
Lecture 1
Slide 72
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 72
Alternating Current and Household Circuits
• If we plot the voltage across an electrical outlet as a
function of time, we get another sinusoidal curve.
– The effective value of this voltage is typically between 110 and
120 volts in North America.
– The standard household power supplied in this country is 115
volts, 60 hertz ac.
– Household circuits are wired in parallel so that different
appliances can be added to or removed from the circuit
without affecting the voltage available.
Introduction
Section 0
Lecture 1
Slide 73
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 73
Alternating Current and Household Circuits
A 60-W light bulb is designed to operate on 120 V ac. What is the
effective current drawn by the bulb?
a)
b)
c)
d)
e)
P  60 W
0.2 A
0. 5 A
2.0 A
72 A
7200 A
Introduction
Veffective  120 V
P  IV 
I
Section 0
Lecture 1
Slide 74

Fall 2004
Spring 2009
60 W
120 V
 0.5 A
INTRODUCTION TO Modern Physics PHYX 2710
Physics of Technology—PHYS 1800
P
V
Waves
Lecture 35 Slide 74
Alternating Current and Household Circuits
• Household circuits are wired in parallel so that different
appliances can be added to or removed from the circuit
without affecting the voltage available.
– As you add more appliances, the total current drawn
increases, because the total effective resistance of the circuit
decreases when resistances are added in parallel.
– Since too large a current could cause the wires to overheat, a
fuse or circuit breaker in series with one leg of the circuit will
disrupt the circuit if the current gets too large.
– Appliances with larger power requirements (stoves, clothes
dryers, etc) are usually connected to a separate 220-V line.
Introduction
Section 0
Lecture 1
Slide 75
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 75
Generators
– The flux changes continuously from a maximum value in one
direction, to zero, to a maximum value in the opposite
direction.
– The induced voltage depends on the rate of change of the
flux.
– When the flux is
increasing the fastest,
the voltage is a
maximum; when the
flux is decreasing the
fastest, the voltage is
a maximum in the
other direction
(negative).
Introduction
Section 0
Lecture 1
Slide 76
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 76
Physics of Technology
PHYS 1800
Lecture 35
Waves
Introduction
Section 0
Lecture 1
Slide 77
Review of Oscillations
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 77
Magnets and the Magnetic Force
• We are generally more familiar with
magnetic forces than with electrostatic
forces.
• Like the gravitational force and the
electrostatic force, this force acts even
when the objects are not touching one
another.
• Is there a relationship between electrical
effects and magnetism?
• Maxwell discovered that the electrostatic
force and the magnetic force are really just
different aspects of one fundamental
electromagnetic force.
Introduction
Section 0
Lecture 1
James Clerk Maxwell
Slide 78
• Our understanding of that relationship
has led to numerous inventions such as
electric motors, electric generators,
transformers, etc.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 78
Electromagnetic Waves
• Maxwell Equations (1865)
described all of E&M. They predict
the existence of EM waves:
c
1
 o o
 2.998108 m / s
– c is speed of EM waves (light)
• Hetrz (1888) showed EM waves:
–
–
–
–
–
–
–
have speed c
have wavelength
have both E and M components
reflect
Introduction Section 0 Lecture 1 Slide 79
Refract
Interfere
diffract
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 79
What do light, radio waves, microwaves, and X rays have
in common?
a)
b)
c)
d)
e)
They all can travel through empty space.
They all travel at the same speed.
They all have no mass.
All the above are true.
Only answers a and b are true.
Introduction
Section 0
Lecture 1
Slide 80
These are all forms of electromagnetic waves. Although
seemingly quite different, they share many properties,
including a, b, and c.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 80
Electromagnetic Waves
• An electromagnetic wave consists of time-varying electric and
magnetic fields, in directions perpendicular to each other as well
as to the direction the wave is traveling.
Introduction
Section 0
Lecture 1
Slide 81
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 81
Antennas
• The electric and the magnetic fields can be produced by
charged particles.
– An electric field surrounds any charged particle.
– A magnetic field surrounds moving charged particles.
•A rapidly alternating
electric current in a wire
generates magnetic
fields whose direction
and magnitude change
with time.
•This changing
magnetic
field inSection
turn0 Lecture
Introduction
produces a changing
electric field.
1
Slide 82
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 82
Electromagnetic Waves
• Likewise, a changing electric field produces a magnetic
field.
• Maxwell realized a wave involving these fields could
propagate through space:
– A changing magnetic field produces a changing electric field,
which produces a changing magnetic field, etc...
– Thus a transverse wave of associated changing electric and
magnetic fields is produced.
Introduction
Section 0
Lecture 1
Slide 83
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 83
Speed of Light
• Maxwell predicted the speed of electromagnetic waves in a
vacuum using the Coulomb constant k in Coulomb’s law and the
magnetic force constant k in Ampere’s law:
v  k k  3108 m s
• This was equal to the known value for the speed of light!
c  3 108 m s
 for measuring the speed of light
Fizeau’s wheel

Introduction
Section 0
Lecture 1
Slide 84
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 84
Electromagnetic Spectrum
There is a wide spectrum of frequencies and wavelengths of
electromagnetic waves.
– Different types of electromagnetic waves have different wavelengths and
frequencies.
– Together they form the electromagnetic spectrum.
Introduction
Section 0
Lecture 1
Slide 85
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 85
–Since they all travel at the speed of light c in a vacuum, their
frequencies and wavelengths are related by: v = c = f 
What is the frequency of radio waves with a wavelength of 10 m?
 = 10 m
f=v/
= (3 x 108 m/s) / 10 m
= 3 x 107 Hz
v = c = 3 x 108 m/s
v=f
Introduction
Section 0
Lecture 1
Slide 86
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 86
– Waves in different parts of the electromagnetic spectrum differ not
only in wavelength and frequency but also in how they are
generated and what materials they will travel through.
• Radio waves are generated by accelerated charges in an oscillating electrical
circuit.
• X rays come from energy transitions of atomic electrons.
• Gamma rays originate inside an atomic nucleus.
• Infrared light is radiated by all warm bodies.
• Oscillating atoms within the molecules of the warm body serve as the antennas.
• X rays will pass through materials that are opaque to visible light.
• Radio waves will pass through walls that light cannot penetrate.
Introduction
Section 0
Lecture 1
Slide 87
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 87
– Different wavelengths of visible light are associated with different
colors.
•
•
•
•
•
Violet is about 3.8 x 10-7 m.
Wavelengths shorter than the violet comprise ultraviolet light.
Red is about 7.5 x 10-7 m.
Wavelengths longer than the red comprise infrared light.
In between, the colors are red, orange, yellow, green, blue, indigo, and
violet.
Introduction
Section 0
Lecture 1
Slide 88
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 88
Wavelength and Color
 How do we perceive
?
 What causes different objects to have
 Why is the sky
Introduction
Section 0
?
?
Lecture 1
Slide 89
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 89
Newton demonstrated that white light is a mixture of colors.
– He showed that white light from the sun, after being split into different colors by
one prism, can be recombined by a second prism to form white light again.
Introduction
Section 0
Lecture 1
Slide 90
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 90
Physics of Technology
Next Lab/Demo:
Electric Circuits
Magnetism
Thursday 1:30-2:45
ESLC 46
Ch 13 and 14
Next Class:
Friday 10:30-11:20
BUS
Slide 91318 room
Read Ch 14
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Waves
Lecture 35 Slide 91