Question

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?

Answer 1

`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.

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.