   Chapter 14, Problem 27P

Chapter
Section
Textbook Problem

A commuter train passes a passenger platform at a constant speed of 40.0 m/s. The train horn is sounded at its characteristic frequency of 320. Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (b) What wavelength is detected by a person on the platform as the train approaches?

(a)

To determine
Change in frequency is detected by a person on the platform as the train moves from approaching to receding.

Explanation

Given Info: Frequency of train horn is 320 Hz and velocity of train is 40 m/s.

Formula for frequency of a horn heard while the train is approaching is,

(f0)approa=fs(v+v0vvs)

• (f0)approa  is frequency of a horn heard while the train is approaching.
• v0 is the velocity of person on the platform.
• v is the speed of the sound.
• vs is the velocity of train.

Substitute 320 Hz for fs , 0 m/s for v0 and 40 m/s for vs and 343 m/s for v in the above expression to get (f0)approa .

(f0)approa=320Hz(343m/s+0m/s343m/s40m/s)=362Hz

Formula for frequency of horn heard while the train is receding is,

(f0)rece=fs(v+v0vvs)

• (f0)rece  is frequency of horn heard while the train is receding.

Since the train is receding the sound source, the velocity of the train is 40m/s . Negative sign indicates recession

(b)

To determine
The wavelength detected by a person on the platform as the train approaches.

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