Mastering Physics Solutions: The Doppler Effect on a Train

The Doppler Effect on a Train

Part A = fapproach = 302Hz
Part B = frecede = 228Hz

Solutions Below:

A train is traveling at 30.0 m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz.

The speed of sound in air should be taken as 344 m/s.

Part A

What frequency fapproach is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?

The formula to calculate the perceived frequency due to the Doppler effect is given by:

fperceived = fsource*(vsound + vlistener) / (vsound + vsource)

Make sure to keep the signs of the source and listener velocities straight – the listener is always on the “left” and the sound source is always on the “right”. So if the two are approaching, the sign for the listener’s velocity is positive and the sign for the source’s velocity is negative.

So:

fperceived = fsource*(vsound + vlistener) / (vsound + vsource)
fperceived = 262*(344 + 18) / (344 – 30)

fperceived = 302 Hz

Part B

What frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Be careful with this problem – MasteringPhysics is actually unclear in what it’s asking for here, so make sure to pay attention to the way the formula is set up in order to get the answer that MasteringPhysics wants.

For this problem everything is the same as Part A, except the directions of the listener and source are reversed (e.g. the signs flip since both are moving away from each other)

fperceived = fsource*(vsound + vlistener) / (vsound + vsource)
fperceived = 262*(344 – 18) / (344 + 30)

fperceived = 228 Hz

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