Chapter 2: Q43E (page 541)
Two organ pipes, open at one end but closed at the other, are each long. One is now lengthened by . Find the beat frequency that they produce when playing together in their fundamentals.
The beat frequency came out to be .
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A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32 m/s, and the crests of the waves ahead of the duck are spaced 0.12 m apart. (a) What is the duck’s speed? (b) How far apart are the crests behind the duck?
Two train whistles, A and B, each have a frequency of 393Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35m/s. A listener is between the two whistles and is moving toward the right with a speed of 15m/s. No wind is blowing. (a) What is the frequency from A as heard by the listener? (b) What is the frequency from B as heard by the listener? (c) What is the beat frequency detected by the listener?
Singing in the Shower. A pipe closed at both ends can have standing waves inside of it, but you normally don’t hear them because little of the sound can get out. But you can hear them if you are inside the pipe, such as someone singing in the shower. (a) Show that the wavelengths of standing waves in a pipe of length L that is closed at both ends are and the frequencies are given by , where n = 1, 2, 3, c.(b) Modelling it as a pipe, find the frequency of fundamental and the first two overtones for a shower 2.50 m tall. Are these frequencies audible?
A turntable 1.50 m in diameter rotates at 75 rpm. Two speakers, each giving off sound of wavelength 31.3 cm, are attached to the rim of the table at opposite ends of a diameter. A listener stands in front of the turntable. (a) What is the greatest beat frequency the listener will receive from this system? (b) Will the listener be able to distinguish individual beats?
A violinist is tuning her instrument to concert A . She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of , which increases to when she tightens her violin string slightly. (a) What was the frequency of the note played by her violin when she heard the beats? (b) To get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the beats?
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