CHAPTER 12: 2, 3, 5, 6, 7, 8, 11, 13, 14, 15, 17, 19, 20, 21, 22, 25, 27, 29, 30, 32, 34, 36, 37, 40, 41, 43,
44.
2. Frequency and period are reciprocals of one another; f = 1/T, and T = 1/f. Double one and the other is half as
much. So doubling the frequency of a vibrating object halves the period.
3. As you dip your fingers more frequently into still water, the waves you produce will be of a higher frequency
(we see the relationship between “how frequently” and “frequency”). The crests of the higher-frequency waves
will be closer together—their wavelengths will be shorter.
5. Shake the garden hose to-and-fro in a direction perpendicular to the hose to produce a sine-like curve.
6. To produce a transverse wave with a Slinky, shake it to-and-fro in a direction that is perpendicular to the
length of the Slinky itself (as with the garden hose in the previous exercise). To produce a longitudinal wave,
shake it back-and-forth along the direction of its length, so that a series of compressions and rarefactions is
produced.
7. The fact that gas can be heard escaping from a gas tap before it is smelled indicates that the pulses of
molecular collisions (the sound) travel more quickly than the molecules migrate. (There are three speeds to
consider: (1) the average speed of the molecules themselves, as evidenced by temperature—quite fast, (2) the
speed of the pulse produced as they collide—about 3⁄4 the speed of the molecules themselves, and (3) the very
much slower speed of molecular migration.)
8. The shorter wavelengths are heard by bats (higher frequencies have shorter wavelengths).
11. The wavelength of the electromagnetic wave will be much longer because of its greater
speed. You can see this from the equation speed = wavelength  frequency, so for the same
frequency greater speed means greater wavelength. Or you can think of the fact that in the
time of one period—the same for both waves—each wave moves a distance equal to one
wavelength, which will be greater for the faster wave.
12. Light travels about a million times faster than sound in air, so you see a distant event a
million times sooner than you hear it.
13. The electronic starting gun does not rely on the speed of sound through air, which favors closer runners, but
gets the starting signal to all runners simultaneously.
14. At the instant that a high-pressure region is created just outside the prongs of a tuning fork, a low-pressure
region is created between the prongs. This is because each prong acts like a Ping-Pong paddle in a region full
of Ping-Pong balls. Forward motion of the paddle crowds Ping-Pong balls in front of it, leaving more space
between balls in back of it. A half-cycle later when the prongs swing in toward the center, a high-pressure
region is produced between the prongs and a low-pressure region is produced just outside the prongs.
15. Because snow is a good absorber of sound, it reflects little sound—which is responsible for the quietness.
16. The fact that we can see a ringing bell but can’t hear it indicates that light is a distinctly different phenomenon
than sound. When we see the vibrations of the “ringing” bell in a vacuum, we know that light can pass through
a vacuum. The fact that we can’t hear the bell indicates that sound does not pass through a vacuum. Sound
needs a material medium for its transmission; light does not.
17. The Moon is described as a silent planet because it has no atmosphere to transmit sounds.
18. The pitch of the tapped glass decreases as the glass is filled. As the mass of the system (glass plus water)
increases, its natural frequency decreases. For systems of a given size, more mass usually means lower
frequency. This can be seen on a guitar, where the most massive string has the lowest natural pitch. (If you’ve
answered this exercise without actually trying it, shame on you!)
19. If the speed of sound were different for different frequencies, say, faster for higher frequencies, then the farther
a listener is from the music source, the more jumbled the sound would be. In that case, higher-frequency notes
would reach the ear of the listener first. The fact that this jumbling doesn’t occur is evidence that sounds of all
frequencies travel at the same speed. (Be glad this is so, particularly if you sit far from the stage, or if you like
outdoor concerts.)
20. If the frequency of sound is doubled, its speed will not change at all, but its wavelength will be “compressed”
to half size. The speed of sound depends only on the medium through which it travels, not on its frequency,
wavelength, or intensity (until the intensity gets so great that a shock wave results).
21. Sound travels faster in warm air because the air molecules that compose warm air themselves travel faster and
therefore don’t take as long before they bump into each other. This lesser time for the molecules to bump
against one another results in a faster speed of sound.
22. Sound travels faster in moist air because the less massive water vapor molecules, H 2O, travel faster than the
more massive N2 and O2 molecules at the same temperature. This faster speed results in sound traveling faster.
25. The rule is correct: This is because the speed of sound in air (340 m/s) can be rounded off to
1
⁄3 km/s. Then, from distance = speed  time, we have distance = (1⁄3) km/s  (number of
seconds). Note that the time in seconds divided by 3 gives the same value.
27. Marchers at the end of a long parade will be out of step with marchers nearer the band because time is required
for the sound of the band to reach the marchers at the end of a parade. They will step to the delayed beat they
hear.
29. A harp produces relatively softer sounds than a piano because its sounding board is smaller and lighter.
30. The sound is louder when a struck tuning fork is held against a table because a greater surface is set into
vibration. In keeping with the conservation of energy, this reduces the length of time the fork keeps vibrating.
Loud sound over a short time spends the same energy as weak sound for a long time.
32. These noise-canceling devices use interference to cancel the sound of the jackhammer in the ears of its
operator. Because of the resulting low jackhammer noise in the ears of the operator, he can hear your voice
clearly. But you, however, without the earphones experience no such cancellation of sound, so the voice of the
operator is drowned out by the loud jackhammer noise.
34. The “beat frequency” is 2 per minute, so you and your friend will be in step twice per minute, or every 30
seconds. You can see this also from the fact that your friend’s stride length is a little shorter than yours, 24⁄25 as
long to be exact, so when you have taken exactly 24 strides—which is after half a minute—your friend will
have taken exactly 25 and you will be back in step.
36. (a) The frequency increases.
(b) The wavelength decreases.
(c) The speed is unchanged (because the air remains motionless relative to you).
37. No, the effects of shortened waves and stretched waves would cancel one another.
40. Oops, careful. The Doppler effect is about changes in frequency, not speed.
41. The conical angle of a shock wave becomes narrower with greater speeds. We see this in the sketches:
43. A shock wave and the resulting sonic boom are produced whenever an aircraft is supersonic, whether or not
the aircraft has just become supersonic or has been supersonic for hours. It is a popular misconception that
sonic booms are principally produced at the moment an aircraft becomes supersonic. This is akin to saying that
a boat produces a bow wave at the moment it exceeds the wave-speed of water. It begins to produce a bow
wave at this crucial moment, but if it moved no faster, the overlapping pattern of waves would not extend very
far from the bow. Likewise with an aircraft. Both the boat and the aircraft must appreciably exceed wave speed
to produce an ample bow and shock wave.
44. The speed of the sound source rather than the loudness of the sound is crucial to the production of a shock
wave. At subsonic speeds, no overlapping of the waves will occur to produce a shock wave. Hence no sonic
boom is produced.