A commuter train passes a passenger platform at a constant speed of 40.0 m/s. The train horn is sounded at its frequency of 320 Hz. What wavelength is detected by a person on the platform as the train approaches?

1 Answer
Michael
Dec 7, 2015

#lambda_(obs)=0.949"m"#

Explanation:

I'll assume 20 degC for which the speed of sound is #343.7"m/s"#

This is an example of the Doppler Effect.

For the person standing on the platform, more wavefronts are arriving per second so he or she will detect sound of a shorter wavelength and higher frequency.

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If the source is approaching the observed wavelength is given by:

#lambda_(obs)=((v-v_s))/f_("source")#

Putting in the numbers:

#lambda_(obs)=((343.7-40))/320=0.949"m"#

You can compare this to the note which someone would hear on the train:

#lambda=v/f=343.7/320=1.07"m"#

So you can see that the person on the platform detects a slightly shorter wavelength and a slightly higher frequency of note.

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