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Chapter 2: Q47E (page 541)

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?

Short Answer

Expert verified

a) 375Hz

b) 370.75Hz

c) 4 Hz

Step by step solution

01

Doppler’s effect

The Doppler’s effect is given by the formula, fL=v+vLv+sfs, where

  • fLis the frequency observed by the listener.
  • vis the speed of sound.
  • vLis the speed of the listener.
  • vsis the speed of the source of sound.
  • vsis the frequency of the source of sound.
02

Calculate frequency when the listener is moving away from the source

fL=v+vLv+vSfSfL=344-15344+0×392fL=375Hz

03

Calculate frequency when listener is moving towards the source and source is moving away from the listener

fL=v+vLv+vSfSfL=344+15344+35×392fL=370.75Hz

04

Calculate beat

beat=|f1-f2|beat=|375-370.75|beat=4Hz

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Most popular questions from this chapter

A railroad train is traveling at 25m/s in still air. The frequency of the note emitted by the locomotive whistle is 400Hz. What is the wavelength of the sound waves (a) in front of the locomotive and (b) behind the locomotive? What is the frequency of the sound heard by a stationary listener (c) in front of the locomotive and (d) behind the locomotive?

BIO For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0×10-5Pa. Calculate the (a) intensity; (b) sound intensity level; (c) displacement amplitude of this sound wave at 20°C.

The longest pipe found in most medium-size pipe organs is 4.88 m (16 ft) long. What is the frequency of the note corresponding to the fundamental mode if the pipe is (a) open at both ends, (b) open at one end and closed at the other?

The frequency of the note F4 is 349 Hz. (a) If an organ pipe is open at one end and closed at the other, what length must it have for its fundamental mode to produce this note at 20.0°C? (b) At what air temperature will the frequency be 370 Hz, corresponding to a rise in pitch from F to F-sharp? (Ignore the change in length of the pipe due to the temperature change.)

A long tube contains air at a pressure of 1.00 atm and a temperature of 77.0°C. The tube is open at one end and closed at the other by a movable piston. A tuning fork that vibrates with a frequency of 500 Hz is placed near the open end. Resonance is produced when the piston is at distances 18.0 cm, 55.5 cm, and 93.0 cm from the open end. (a) From these values, what is the speed of sound in air at 77.0°C? (b) From the result of part (a), what is the value of g? (c) These results show that a displacement antinode is slightly outside the open end of the tube. How far outside is it?
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