Problem 11: Suppose a train that has a 150 Hz horn is moving at 35.0 m/s in still air on a day when the speed of sound is 340 m/s. (a) What frequencies are observed by a stationary person at the side of the track as the train approaches and after it passes? (b) What frequency is observed by the train’s engineer traveling on the train?

Solution

Given

Frequency of the sound = f = 150 Hz,

Velocity of the sound, v = 340 ms^{-1}

Velocity of the train = a = 35 ms^{-1}

Required

Frequency of the sound when train is approaching the listener, f_{1}

Frequency of the sound after the train passes the listener, f_{2}

Frequency observed by the engineer in the train

– In this case, the train (or the sounding source) is approaching to the stationary listener. Therefore, we use the formula,

Put values,

When the train passes the stationary listener, the sounding source is moving away from the stationary listener and we use the formula,

Now put the values,

There will be no apparent change in frequency for the engineer in the train. The sounding source (horn) and listener (engineer) both are in the same system of reference.

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