Chapter 11 assignment

Answers to selected problems for Chapter 11 are found here.

Exercise 14. In an Olympic competition, a microphone picks up the sound of the starter's gun and sends it elecrically to speakers at every runner's starting block. Why?
Because the speed of sound is much slower than the speed of electricity, this reduces the split-second delay between firing the gun and the sound reaching the runner furthest away from the gun.
Exercise 26. A rule of thumb for estimating the distance in kilometers between an observer and a lightning stroke is to divide the number of seconds in the interval between the flash and the sound by 3. Is this rule correct?
The speed of sound in air is between 330 and 340 m/s; the speed of light is 300 million m/s; that means that, for all practical purposes, the speed of light is instantaneous (a million times faster than sound). So we see the flash at essentially the same moment it happens. However, the sound takes three seconds to cover a kilometer: 1000 meters ÷ 333 m/s = 3 seconds. Therefore, the approximate rule (3 seconds per kilometer) is correct.

Since there are 1.6 km per mile, to get miles, divide the number of seconds between flash and sound by five.
Exercise 32. The sitar, an Indian musical instrument, has a set of strings that vibrate and produce music, even though they are never plucked by the player. These "sympathetic strings" are identical to the plucked strings and are mounted below them. What is your explanation?
Vibrations in the plucked strings generate sound waves that cause the sympathetic strings to vibrate at the same frequencies.
Exercise 34. Two sound waves of the same frequency can interfere with one another, but two sound waves must have different frequencies in order to make beats. Why?
If sound waves have the same frequency, they can be totally in phase, totally out of phase, or anything in between, but their waves always either reinforce or cancel each other, so that the "summed sound" is either louder or softer than the individual sounds. But if the two sound waves are of different frequencies, they cancel each other except when their crests coincide; this amplification produces the "beat" phenomenon.
Exercise 38. When you blow your horn while driving toward a stationary listener, an increase in frequency of the horn is heard by the listener. Would the listener hear an increase in the frequency of the horn if he were also in a car traveling at the same speed in the same direction as you are? Explain.
No. The doppler effect is caused by wave crests from the emitter reaching the observer either faster or slower than they "should" and is caused by the observer having some velocity with respect to the emitter. But if the emitter and observer have identical velocities, they are not moving relative to one another and there is no doppler effect.
Exercise 40. How does the Doppler effect aid police in detecting speeding motorists?
The radar waves are bounced back to the receiver from the motorist. The bounce-back will not be at the same frequency as the emitted wave unless the motorist is not moving at all relative to the transmitter; otherwise, the wave crests will bounce either more or less rapidly than their frequency, depending on whether the motorist is approaching or moving away from the receiver.
Exercise 44. If the sound of an airplane does not originate in the part of the sky where the plane is seen, does this imply that the airplane is traveling faster than the speed of sound? Explain.
No. The speed of sound is so much slower than the speed of light that an airplane (throwing out, say, a firecracker at point A) will have moved a visible distance (to point B) before the sound can reach the ground. Since the sound comes from point A and the airplane's observed position is point B, we will perceive the sound as coming from behind the airplane.
Problem 9. For years, marine scientists were mystified by sound waves detected by underwater microphones in the Pacific Ocean. These so-called T waves were among the purest sounds in nature. Eventually the researchers traced the source to underwater volcanoes whose rising columns of bubbles resonated like organ pipes. What is the wavelength of a typical T wave whose frequency is 7 Hz? (The speed of sound in seawater is 1530 m/s.)

Speed = wavelength × frequency. Therefore, the wavelength is equal to the speed of sound in seawater divided by the frequency, that is, 1530 m/s ÷ 7 Hz = 219 meters.
Problem 14. What beat frequencies are possible with tuning forks of frequencies 256, 259, and 261 Hz?

  • The 259-Hz and 261-Hz forks will beat at 2 Hz (261 minus 259).
  • The 256-Hz and 259-Hz forks will beat at 3 Hz.
  • The 256-Hz and 261-Hz forks will beat at 5 Hz.