Chapter 20. Traveling Waves
You may not realize it, but
you are surrounded by
waves. The “waviness” of a
water wave is readily
apparent, from the ripples on
a pond to ocean waves large
enough to surf. It’s less
apparent that sound and light
are also waves.
Chapter Goal: To learn the
basic properties of traveling
waves.
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Chapter 20. Traveling Waves
Topics:
• The Wave Model
• One-Dimensional Waves
• Sinusoidal Waves
• Waves in Two and Three Dimensions
• Sound and Light
• Power, Intensity, and Decibels
• The Doppler Effect
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Chapter 20. Reading Quizzes
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A graph showing wave displacement
versus position at a specific instant of
time is called a
A. snapshot graph.
B. history graph.
C. bar graph.
D. line graph.
E. composite graph.
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A graph showing wave displacement
versus position at a specific instant of
time is called a
A. snapshot graph.
B. history graph.
C. bar graph.
D. line graph.
E. composite graph.
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A graph showing wave displacement
versus time at a specific point in space
is called a
A. snapshot graph.
B. history graph.
C. bar graph.
D. line graph.
E. composite graph.
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A graph showing wave displacement
versus time at a specific point in space
is called a
A. snapshot graph.
B. history graph.
C. bar graph.
D. line graph.
E. composite graph.
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A wave front diagram shows
A. the wavelengths of a wave.
B. the crests of a wave.
C. how the wave looks as it moves
toward you.
D. the forces acting on a string that’s
under tension.
E. Wave front diagrams were not
discussed in this chapter.
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A wave front diagram shows
A. the wavelengths of a wave.
B. the crests of a wave.
C. how the wave looks as it moves
toward you.
D. the forces acting on a string that’s
under tension.
E. Wave front diagrams were not
discussed in this chapter.
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The waves analyzed in this chapter are
A. string waves.
B. sound and light waves.
C. sound and water waves.
D. string, sound, and light waves.
E. string, water, sound, and light waves.
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The waves analyzed in this chapter are
A. string waves.
B. sound and light waves.
C. sound and water waves.
D. string, sound, and light waves.
E. string, water, sound, and light waves.
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Chapter 20. Basic Content and Examples
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Transverse and Longitudinal Waves
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Transverse and Longitudinal Waves
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Wave Speed
The speed of transverse waves on a string stretched with
tension Ts is
where µ is the string’s mass-to-length ratio, also called the
linear density.
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EXAMPLE 20.1 The speed of a wave pulse
QUESTION:
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EXAMPLE 20.1 The speed of a wave pulse
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EXAMPLE 20.1 The speed of a wave pulse
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EXAMPLE 20.1 The speed of a wave pulse
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EXAMPLE 20.1 The speed of a wave pulse
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One-Dimensional Waves
• To understand waves we must deal
with functions of two variables, position and
time.
• A graph that shows the wave’s displacement as
a function of position at a single instant of time
is called a snapshot graph. For a wave on a
string, a snapshot graph is literally a picture of
the wave at this instant.
• A graph that shows the wave’s displacement as
a function of time at a single position in space
is called a history graph. It tells the history of
that particular point in the medium.
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EXAMPLE 20.2 Finding a history graph from
a snapshot graph
QUESTION:
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EXAMPLE 20.2 Finding a history graph from
a snapshot graph
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EXAMPLE 20.2 Finding a history graph from
a snapshot graph
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EXAMPLE 20.2 Finding a history graph from
a snapshot graph
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EXAMPLE 20.2 Finding a history graph from
a snapshot graph
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Sinusoidal Waves
• A wave source that oscillates with simple
harmonic motion (SHM) generates a sinusoidal wave.
• The frequency f of the wave is the frequency of
the oscillating source.
• The period T is related to the wave frequency f by
• The amplitude A of the wave is the maximum value
of the displacement. The crests of the wave
have displacement Dcrest = A and the troughs have
displacement Dtrough = −A.
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Sinusoidal Waves
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Sinusoidal Waves
• The distance spanned by one cycle of the motion is
called the wavelength λ of the wave. Wavelength is
measured in units of meters.
• During a time interval of exactly one period T, each
crest of a sinusoidal wave travels forward a distance of
exactly one wavelength λ.
• Because speed is distance divided by time, the
wave speed must be
or, in terms of frequency
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Sinusoidal Waves
• The angular frequency of a wave is
• The wave number of a wave is
• The general equation for the displacement caused
by a traveling sinusoidal wave is
This wave travels at a speed v = ω/k.
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Waves in Two and Three Dimensions
• Suppose you were to take a photograph of
ripples spreading on a pond. If you mark the
location of the crests on the photo, these would be
expanding concentric circles. The lines that locate
the crests are called wave fronts, and they are
spaced precisely one wavelength apart.
• Many waves of interest, such as sound waves
or light waves, move in three dimensions.
For example, loudspeakers and light bulbs
emit spherical waves.
• If you observe a spherical wave very, very far
from its source, the wave appears to be a plane
wave.
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Waves in Two and Three Dimensions
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Waves in Two and Three Dimensions
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Sound Waves
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Sound Waves
• For air at room temperature (20°C), the speed of
sound is vsound = 343 m/s.
• Your ears are able to detect sinusoidal sound
waves with frequencies between about 20 Hz and
about 20,000 Hz, or 20 kHz.
• Low frequencies are perceived as “low pitch”
bass notes, while high frequencies are heard as “high
pitch” treble notes.
• Sound waves exist at frequencies well above 20
kHz, even though humans can’t hear them. These are
called ultrasonic frequencies.
• Oscillators vibrating at frequencies of many
MHz generate the ultrasonic waves used in
ultrasound medical imaging.
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EXAMPLE 20.6 Sound wavelengths
QUESTION:
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EXAMPLE 20.6 Sound wavelengths
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EXAMPLE 20.6 Sound wavelengths
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EXAMPLE 20.6 Sound wavelengths
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Electromagnetic Waves
• A light wave is an electromagnetic wave, an
oscillation of the electromagnetic field.
• Other electromagnetic waves, such as radio
waves, microwaves, and ultraviolet light, have the
same physical characteristics as light waves even though
we cannot sense them with our eyes.
• All electromagnetic waves travel through vacuum
with the same speed, called the speed of light. The value
of the speed of light is c = 299,792,458 m/s.
• At this speed, light could circle the earth 7.5 times in
a mere second—if there were a way to make it go
in circles!
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The Index of Refraction
• Light waves travel with speed c in a vacuum, but
they slow down as they pass through transparent
materials such as water or glass or even, to a very
slight extent, air.
• The speed of light in a material is characterized by
the material’s index of refraction n, defined as
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Power and Intensity
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EXAMPLE 20.9 The intensity of a laser beam
QUESTION:
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EXAMPLE 20.9 The intensity of a laser beam
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EXAMPLE 20.9 The intensity of a laser beam
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EXAMPLE 20.9 The intensity of a laser beam
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Intensity and Decibels
• Human hearing spans an extremely wide range
of intensities, from the threshold of hearing at ≈ 1 ×
10−12 W/m2 (at midrange frequencies) to the threshold
of pain at ≈ 10 W/m2.
• If we want to make a scale of loudness, it’s
convenient and logical to place the zero of our scale at
the threshold of hearing.
• To do so, we define the sound intensity level,
expressed in decibels (dB), as
where I0 = 1 × 10−12 W/m2.
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Intensity and Decibels
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The Doppler Effect
• An interesting effect occurs when you are
in motion relative to a wave source. It is called
the Doppler effect.
• You’ve likely noticed that the pitch of
an ambulance’s siren drops as it goes past you.
A higher pitch suddenly becomes a lower pitch.
• As a wave source approaches you, you will
observe a frequency f+ which is slightly higher than
f0, the natural frequency of the source.
• As a wave source recedes away from you, you
will observe a frequency f− which is slightly lower
than f0, the natural frequency of the source.
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The Doppler Effect
The frequencies heard by a stationary observer when
the sound source is moving at speed v0 are
The frequencies heard by an observer moving at speed
v0 relative to a stationary sound source emitting
frequency f0 are
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EXAMPLE 20.11 How fast are the police
traveling?
QUESTION:
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EXAMPLE 20.11 How fast are the police
traveling?
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EXAMPLE 20.11 How fast are the police
traveling?
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EXAMPLE 20.11 How fast are the police
traveling?
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Chapter 20. Summary Slides
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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Applications
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Applications
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Applications
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Chapter 20. Questions
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Which of the following actions would make
a pulse travel faster down a stretched
string?
A. Use a heavier string of the same length,
under the same tension.
B. Use a lighter string of the same length,
under the same tension.
C. Move your hand up and down more
quickly as you generate the pulse.
D. Move your hand up and down a larger
distance as you generate the pulse.
E. Use a longer string of the same thickness,
density, and tension.
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Which of the following actions would make
a pulse travel faster down a stretched
string?
A. Use a heavier string of the same length,
under the same tension.
B. Use a lighter string of the same length,
under the same tension.
C. Move your hand up and down more
quickly as you generate the pulse.
D. Move your hand up and down a larger
distance as you generate the pulse.
E. Use a longer string of the same thickness,
density, and tension.
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The graph at the top is the history graph
at x = 4 m of a wave traveling to the right
at a speed of 2 m/s. Which is the history
graph of this wave at x = 0 m?
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The graph at the top is the history graph
at x = 4 m of a wave traveling to the right
at a speed of 2 m/s. Which is the history
graph of this wave at x = 0 m?
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What is the
frequency of this
traveling wave?
A. 0.1 Hz
B. 0.2 Hz
C. 2 Hz
D. 5 Hz
E. 10 Hz
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What is the
frequency of this
traveling wave?
A. 0.1 Hz
B. 0.2 Hz
C. 2 Hz
D. 5 Hz
E. 10 Hz
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What is the phase difference between
the crest of a wave and the adjacent
trough?
A. 0
B. π
C. π /4
D. π /2
E. 3 π /2
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What is the phase difference between
the crest of a wave and the adjacent
trough?
A. 0
B. π
C. π /4
D. π /2
E. 3 π /2
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A light wave travels through three
transparent materials of equal thickness.
Rank in order, from the largest to smallest,
the indices of refraction n1, n2, and n3.
A. n1 > n2 > n3
B. n2 > n1 > n3
C. n3 > n1 > n2
D. n3 > n2 > n1
E. n1 = n2 = n3
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A light wave travels through three
transparent materials of equal thickness.
Rank in order, from the largest to smallest,
the indices of refraction n1, n2, and n3.
A. n1 > n2 > n3
B. n2 > n1 > n3
C. n3 > n1 > n2
D. n3 > n2 > n1
E. n1 = n2 = n3
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Four trumpet players are playing the same
note. If three of them suddenly stop, the
sound intensity level decreases by
A. 4 dB
B. 6 dB
C. 12 dB
D. 40 dB
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Four trumpet players are playing the same
note. If three of them suddenly stop, the
sound intensity level decreases by
A. 4 dB
B. 6 dB
C. 12 dB
D. 40 dB
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Amy and Zack are both listening to the
source of sound waves that is moving to
the right. Compare the frequencies each
hears.
A. fAmy > fZack
B. fAmy < fZack
C. fAmy = fZack
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Amy and Zack are both listening to the
source of sound waves that is moving to
the right. Compare the frequencies each
hears.
A. fAmy > fZack
B. fAmy < fZack
C. fAmy = fZack
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