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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鈥檚 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脳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脳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

In case 1, a source of sound approaches a stationary observer at speed u. In case 2, the observer moves toward the stationary source at the same speed u. If the source is always producing the same frequency sound, will the observer hear the same frequency in both cases, since the relative speed is the same each time? Why or why not?

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