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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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