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The quack researchers speculated that the myth might have
resulted because:
t = 0.10 s 1. The quack does echo, but it is usually too quiet to hear
1 34 m v = 343 m/s because a duck quacks too quietly.
2 • d = 34 m 2. Ducks quack near water, not near reflecting surfaces such
d as a mountain or building that would make an echo.
= 17 m
2
3. It is hard to hear the echo of a sound that fades in and
fades out, as a duck quack does.

A Echo
INTERFERENCE
Waves interact with a boundary much as a particle would, refl ect-
ing or refracting because of the boundary. A moving ball, for
example, will bounce from a surface at the same angle it strikes
the surface, just as a wave does. A particle or a ball, however, can
be in only one place at a time, but waves can be spread over a dis-
t = 1.0 s tance at the same time. You know this since many diff erent people

1 v = 5,023 ft/s in different places can hear the same sound at the same time.
2 • 5,023 ft d = 5,023 ft
1
depth = d
•
2 Constructive and Destructive
When two traveling waves meet, they can interfere with each
other, producing a new disturbance. This new disturbance has

a different amplitude, which is the algebraic sum of the ampli-

B Sonar
tudes of the two separate wave patterns. If the wave crests or wave
FIGURE 5.15 (A) At room temperature, sound travels at troughs arrive at the same place at the same time, the two waves
343 m/s. In 0.10 s, sound will travel 34 m. Since the sound must are said to be in phase. The result of two waves arriving in phase

travel to a surface and back in order for you to hear an echo, the is a new disturbance with a crest and trough that has greater
distance to the surface is one-half the total distance. (B) Sonar displacement than either of the two separate waves. This is called

measures a depth by measuring the elapsed time between an
ultrasonic sound pulse and the echo. The depth is one-half the constructive interference (Figure 5.16A). If the trough of one wave
round trip. arrives at the same place and time as the crest of another wave,
the waves are completely out of phase. When two waves are com-
pletely out of phase, the crest of one wave (positive displacement)
generates an underwater ultrasonic sound pulse, then measures will cancel the trough of the other wave (negative displacement),

the elapsed time for the returning echo. Sound waves travel at and the result is zero total disturbance, or no wave. This is called

about 1,531 m/s (5,023 ft/s) in seawater at 25°C (77°F). A 1 s destructive interference (Figure 5.16B). If the two sets of wave
lapse between the ping of the generated sound and the echo patterns do not have the same amplitudes or wavelengths, they

return would mean that the sound traveled 5,023 ft for the will be neither completely in phase nor completely out of phase.

round trip. The bottom would be one-half this distance below The result will be partly constructive or destructive interference,
the surface (Figure 5.15B). depending on the exact nature of the two wave patterns.
Beats
Myths, Mistakes, and Misunderstandings Suppose that two vibrating sources produce sounds that are
in phase, equal in amplitude, and equal in frequency. Th e
resulting sound will be increased in volume because of con-
A Duck’s Quack Doesn’t Echo?
structive interference. But suppose the two sources are slightly
You may have heard the popular myth that “a duck’s quack different in frequency, for example, 350 and 352 Hz. You will

doesn’t echo, and no one knows why.” An acoustic research ex- hear a regularly spaced increase and decrease of sound known
periment was carried out at the University of Salford in Greater as beats. Beats occur because the two sound waves experience
Manchester, U.K., to test this myth. Acoustic experts first record ed
a quacking duck in a special chamber that was constructed to alternating constructive and destructive interferences ( Figure 5.17).

produce no sound reflections. Simulations were then done in a The phase relationship changes because of the diff erence in
reverberation chamber to match the effect of the duck quacking frequency, as you can see in Figure 5.17. Th ese alternating
when flying past a cliff face. The tests found that a duck’s quack constructive and destructive interference zones are moving
indeed does echo, just like any other sound. from the source to the receiver, and the receiver hears the
results as a rapidly rising and falling sound level. The beat

126 CHAPTER 5 Wave Motions and Sound 5-12