CHAPTER 12
SOUND
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Characteristics of Sound
Intensity of Sound: Decibels
The Ear and Its Response; Loudness
Sources of Sound: Vibrating Strings and Air Columns
Quality of Sound, and Noise; Superposition
Interference of Sound Waves; Beats
Doppler Effect
Shock Waves and the Sonic Boom
Characteristics of Sound
Sound can travel through any kind of matter, but not
through a vacuum.
The speed of sound is different in different materials; in general,
it is slowest in gases, faster in liquids, and fastest in solids.
The speed depends somewhat on temperature, especially for
gases.
The speed of sound in air at 0o Cand 1 atm, is 331 m/s. The
speed increases approximately 0.60 m/s for each Celsius
degree increase in temperature.
v  (331  0.60T )m / s
Unless stated otherwise, assume that the temperature will be:
20o C, so v  [331  (0.60)(20o C)]  343m / s
Loudness: related to intensity of the sound wave
Pitch: related to frequency.
Audible range: about 20 Hz to 20,000 Hz; upper limit decreases with age
Ultrasound: above 20,000 Hz;
Infrasound: below 20 Hz
There are three aspects of any sound:
1. There must be a source for a sound; and as with any wave, the source of a sound must be
a vibrating object.
2. The energy is transferred from the source in the form of longitudinal sound waves
3. The sound is detected by an ear or an instrument
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Sound waves are longitudinal waves traveling through a medium. The tuning fork, a
common device for producing pure notes consists of two metal prongs, or tines,
that vibrate when struck.
Their vibrations disturb the air near them. When a tine swings to the right the
molecules in front of its movement are forced together creating a region of high
molecular density called a compression (condensations).
This compression moves away from the fork like a ripple on a pond. When the tine moves to the
left the molecules in the air spread apart, and the density is lower, called rarefaction (rarefactions).
Example 1: Auto focusing cameras emit a pulse of very high frequency (ultrasonic) sound that
travels to the object being photographed, and include a sensor that detects the returning reflected
sound.
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Calculate the travel time of the pulse for an object 1.0 m away.
Assume the speed of sound at 343 m/s, and the distance is to the subject and back so,
1 m + 1 m = 2 m.
v  d /t
t
d
2.0m

 0.0058s  5.8ms
v 343m / s
Intensity of Sound: Decibels
The intensity of a wave is the energy transported per unit time
across a unit area.
The human ear can detect sounds with intensity as low as 10-12
W/m2 and as high as 1 W/m2.
Perceived loudness, however, is not proportional to the intensity.
The loudness of a sound is much more closely related to the
logarithm of the intensity.
Sound level is measured in decibels (dB) and is defined:
I0 is taken to be the threshold of hearing:
An increase in sound level of 3 dB, which is a doubling
in intensity, is a very small change in loudness.
In open areas, the intensity of sound diminishes with
distance:
However, in enclosed spaces this is complicated by
reflections, and if sound travels through air the higher
frequencies get preferentially absorbed.
The Ear and its Response; Loudness
The ear’s sensitivity varies with frequency. These
curves translate the intensity into sound level at
different frequencies.
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Sources of Sound: Vibrating Strings and Air Columns
Musical instruments produce sounds in various ways – vibrating strings, vibrating membranes,
vibrating metal or wood shapes, vibrating air columns.
The vibration may be started by plucking, striking, bowing, or blowing. The vibrations are
transmitted to the air and then to our ears.
The strings on a guitar can be effectively shortened by fingering,
raising the fundamental pitch.
The pitch of a string of a given length can also be altered by using a
string of different density.
A piano uses both methods to cover its more than sevenoctave range – the lower strings (at bottom) are both
much longer and much thicker than the higher ones.
Example 2: A 0.32-m-long violin string is tuned to play A above middle C at 440 Hz.
a) What is the wavelength of the fundamental string vibration?
  2L
2(0.32m)  0.64m  64cm
This is the wavelength of the standing wave on the string.
b)What is the wavelength of the sound wave produced?
The sound wave that travels outward in the air (to reach our ears) has the same frequency, 440
Hz. The wavelength is:

v 343m / s

 0.78  78cm
f
440Hz
Sources of Sound: Vibrating Strings and Air Columns
Wind instruments create sound through standing waves in a column of air.
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A tube open at both ends (most wind instruments) has pressure nodes, and therefore displacement
antinodes, at the ends.
A tube closed at one end (some organ pipes) has a displacement node (and pressure antinode) at
the closed end.
Example 3: What will be the fundamental frequency and first three overtones for a 26-cm-long
organ pipe at room temperature if it is
a) open?
f1 
v
343m / s

 660Hz
2L 2(0.26m)
1320Hz  1980Hz  2640 Hz
b) closed?
f1 
v
343m / s

 330Hz
4L 4(0.26m)
990 Hz  1650 Hz  2310 Hz
Example 4: A flute is designed to play middle C (262 Hz) as the fundamental frequency when all
the holes are covered. Approximately how long should the distance be from the mouthpiece to the
far end of the flute? Assume room temp.
L
v
343m / s

 0.655m
2 f 2(262s 1 )
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Quality of Sound, and Noise; Superposition
So why does a trumpet sound different from a flute? The answer lies in overtones – which ones are
present, and how strong they are, makes a big difference.
The plot below shows frequency spectra for a clarinet, a piano, and a violin. The differences in
overtone strength are apparent.
Interference of Sound Waves; Beats
Sound waves interfere in the same way that other waves do in space.
A person at a point such as C, which is the same distance from each speaker, will
experience a loud sound – the interference is constructive. At point D little if any
sound – destructive.
Example 5: Two loudspeakers are 1.00 m apart. A person stands 4.00 m from one speaker. How
far must this person be from the second speaker to detect destructive interference when the
speakers emit an 1150-Hz sound?

v 343m / s

 0.30m
f 1150Hz
For destructive interference a person must be one-half wavelength farther from one speaker than
the other, or 0.15m. Thus the person must be 3.85m or 4.15m from 2 nd speaker.
Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow
“envelope” around two waves that are relatively close in frequency.
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Example 6: A tuning fork produces a steady 400 Hz tone. When this tuning fork is struck and held
near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible
frequencies produced by the guitar string?
fbeat  20vibrations / 5s  4Hz
This is the difference of the frequencies of the two waves. Because one wave is 400 Hz the other
must be 404 Hz or 396 Hz.
Doppler Effect
The Doppler Effect occurs when a source of sound is moving with respect to an observer & visa
versa.
At rest both observers hear same frequency. Moving left observer hears lower, right observer
hears higher
If we can figure out what the change in the wavelength is, we also
know the change in the frequency.
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The change in the wavelength is given by:
Source is moving toward the observer.
And the change in the frequency:
If the source is moving away from the observer:
If the observer is moving with respect to the source, things are a bit different. The wavelength
remains the same, but the wave speed is different for the observer.
We find, for an observer moving towards a stationary source:
And if it is moving away:
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Example 7: The siren of a police car at rest emits at a frequency of 1600 Hz. What frequency will
you hear if you are at rest and the police car moves at 25.0 m/s
a) towards you?
f '
f
1600 Hz

 1726 Hz
 vsource   25.0m / s 
1


1 
 
343m / s 
 vsound  
f '
f
1600 Hz

 1491Hz
 vsource   25.0m / s 
1


1 
 
343m / s 
 vsound  
b) away from you?
Example 8: A 5000 Hz sound wave is emitted by a stationary
source. This sound wave reflects from an object moving 3.50
m/s toward the source. What is the frequency of the wave
reflected by the moving object as detected by a detector at rest
near the source?
The frequency f ’ that is detected by the moving object is:

v 
 3.50m / s 
f '  1  obs  f  1 
 (5000 Hz )  5051Hz
343m / s 

 vssnd 
The moving object now emits (reflects) a sound of frequency:
f "
f'
5051Hz

 5103Hz
 vsource   3.50m / s 

1 
 1 
vnd   343m / s 

Thus the frequency shifts by 103 Hz.
Shock Waves and the Sonic Boom
If a source is moving faster than the wave speed in a medium, waves cannot keep up and a shock
wave is formed.
The angle of the cone is:
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Shock waves are analogous to the bow waves produced
by a boat going faster than the wave speed in water.
Aircraft exceeding the speed
of sound in air will produce
two sonic booms, one from
the front and one from the
tail.
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CHAPTER 11/12
WAVES AND VIBRATIONS
CONCEPTS
1. A characteristic common to sound waves and light waves is that they transfer
energy.
2. Light is to brightness as sound is to loudness.
3. A beam of light entering a glass prism obliquely (at an angle) and
emerging as a band of colors illustrates the process of dispersion.
4. The diagram to the right shows white light being dispersed as it
passes from air into a glass prism. This phenomenon occurs because
in glass each frequency of light has a different absolute index of
refraction.
5. A laser beam does not disperse as it passes through a prism because the
laser beam is monochromatic.
6. The diagram to the right represents waves passing through a small
opening in a barrier. This is an example of diffraction.
7. Diffraction and interference will occur when light passes through a
double slit.
8. All electromagnetic waves have the same speed in a vacuum.
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9. The pattern of light produced by the interaction of light with a
thin film is the result of interference.
10. The color spectrum ranges in order from: red, orange, yellow,
green, blue, indigo, and violet.
11. In a nondispersive medium, the speed of light waves depends on the nature of the medium.
12. As the energy imparted to a mechanical wave increases, the maximum displacement
of the particles in the medium increases.
13. A single vibratory disturbance which moves from point to point in a material
is known as a pulse.
14. As a pulse travels through a stretched heavy rope attached to a light
rope its speed will increase as it travels through the light rope.
15. The diagram to the right shows a transverse water wave moving in the
direction shown by the velocity vector v. At the instant shown, a cork
at point P on the water’s surface is moving toward B.
16. Whether or not a wave is longitudinal or transverse may be determined by
its ability to be polarized.
17. As a wave is refracted, the frequency of the wave will remain unchanged.
18. The graph that best represents the relationship between the frequency and
period of a wave is C.
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19. The change in direction of a wave when it passes obliquely from one
medium to another is called refraction.
20. As observed from the Earth, the light from a star is shifted toward lower frequencies. This is an
indication that the distance between the Earth and the star is increasing.
21. As the period of a wave decreases, the wave’s frequency increases.
22. Two waves have the same frequency. They must also have identical periods.
23. In the diagram to the right, the distance between points A and B on a
wave is 0.10 m. This wave must have a wavelength of 0.20 m.
24. As a wave enters a medium, there may be a change in the wave’s speed.
25. Only coherent wave sources produce waves that have a constant phase relation.
26. A sound wave can not be polarized.
27. If the frequency of a sound wave in air at STP remains constant, its energy can be varied by
changing its amplitude.
28. An observer detects an apparent change in the frequency of sound
Waves produced by an airplane passing overhead. This phenomenon
illustrates the Doppler effect.
29. The vibrating tuning fork shown to the right produces a constant frequency.
The tuning fork is moving to the right at a constant speed, and observers
are located at points A, B, C, and D. The observer at D hears the lowest
frequency.
30. Interference occurs when two or more waves pass simultaneously through the same region
in a medium.
31. An opera singer’s voice is able to break a thin crystal glass if the singer’s voice
and the glass have the same natural frequency.
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32. Standing waves are produced by the interference of two waves with the same frequency and
amplitude but opposite directions.
33. When the stretched string of the apparatus on the right is made to
vibrate, point P does not move. Point P is most probably at the location
of a node.
34. The distance between successive antinodes in the standing wave pattern
shown to the right is equal to ½ wavelength.
35. Maximum destructive interference between two waves occurs when the waves are out of phase
by 180 degrees.
36. The diagram on the right represents a group of light waves emitted
simultaneously from a single light source. The light waves would be
classified as both monochromatic and coherent.
37. Refraction of a wave is caused by a change in the wave’s speed.
38. As a periodic wave travels from one medium to another, the period and frequency of that wave
cannot change.
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