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Chapter 17: 2. (page 482)
If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants?
All the energy at those instants is in the form of Kinetic energy.
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An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it’s too dangerous to go inside. Recalling your recent physics class, you decide to try setting up standing-wave resonances inside the tunnel. Using your subsonic amplifier and loudspeaker, you find resonances at 4.5 Hz and 6.3 Hz, and at no frequencies between these. It’s rather chilly inside the tunnel, so you estimate the sound speed to be 335 m/s. Based on your measurements, how far is it to the end of the tunnel?
Two loudspeakers in a plane, 5.0 m apart, are playing the same frequency. If you stand 12.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 12.0 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers. What is the frequency of the sound? Assume a sound speed of 340 m/s.
Two in-phase loudspeakers, which emit sound in all directions,
are sitting side by side. One of them is moved sideways by 3.0 m, then forward by 4.0 m. Afterward, constructive interference is
observed and of the distance between the speakers along the line that joins them. What is the maximum possible wavelength of the sound waves?
Noise-canceling headphones are an application of destructive
interference. Each side of the headphones uses a microphone to
pick up noise, delays it slightly, then rebroadcasts the noise next
to your ear where it can interfere with the incoming sound wave
of the noise. Suppose you are sitting 1.8 m from an annoying,
110 Hz buzzing sound. What is the minimum headphone delay, in
ms, that will cancel this noise?
a. What are the three longest wavelengths for standing waves on a 240-cm-long string that is fixed at both ends? b. If the frequency of the second-longest wavelength is 50 Hz, what is the frequency of the third-longest wavelength?
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