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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car’s horn. A passenger in the back of the train hears the horn’s sound at a frequency of 428 Hz and a passenger in the front hears it at 402 Hz. Find (a) the train’s speed and (b) the horn’s frequency, assuming the sound travels along the tracks.

(a)

To determine
The speed of the train

Explanation

Given Info: frequency of horn in the back of the train is 428 Hz, frequency of passenger in the front of the train is 402 Hz and velocity of sound is 343m/s.

The front of the train is moves away from the sound source and the rear part moves towards the sound source.

Formula for frequency of a back of the train,

fback=fs(v+v0v) (1)

  • fback  is frequency of sound heard at the back of the train.
  • v0 is the velocity of train.
  • v is the speed of the sound.
  • vs is the velocity of the observer.

Formula for frequency of front of the train

ffront=fs(vv0v) (2)

  • ffront  is frequency of sound heard at the front of the train.

Negative sign indicates moving away from the source.

Divide equation (1) and equation (2) to rearrange the expression in terms of

fbackffront=fs(v+v0v)fs

(b)

To determine
The horn's frequency, assuming the sound travels along the tracks

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