A train moves at 45 mph on a track that is very close to, and parallel to a side

Question

A train moves at 45 mph on a track that is very close to, and parallel to a side road. It blows its whistle, which has a pitch of 500. Hz. The speed of sound in air is 343 m/s.

(a) A person is standing on the side of the road. What frequencies does a person hear for the whistle if the train is coming toward, or going away from them?

(b) A car is driving on the road in the direction opposite the train at 45 mph. What frequencies does a person in this car hear, if the train is coming toward, or going away from them?

Explanation / Answer

speed of the train=20.1 m/s

a)by doppler's equaiton,

if coming towards,

f'=500*(343/(343-20.1))

=531.124 Hz

if going away,

f'=500*343/(343+20.1)

=472.322 Hz

c)if coming towards,

f'=500*((343+20.1)/(343-20.1))

=562.248 Hz

if going away,

f'=500*((343-20.1)/(343+20.1))

=444.643 Hz

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