   Chapter 14, Problem 31P

Chapter
Section
Textbook Problem

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 465 Hz when the train is approaching him and 441 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find?

To determine
The speed of the train.

Explanation

Given Info: Frequency of train whistle is 465 Hz, frequency whistle head while train is approaching is 441Hz and velocity of sound is 343m/s.

Formula for frequency of whistle heard while the train is approaching is,

fappro=fs(v+v0vvs) (1)

• fappro is frequency of approaching 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 receding train

freced=fs(vv0vvs) (2)

• freced  is frequency of front of the train.

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

fapprofreced=fs(vvvs)fs

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