Conceptual Physics

16.8 - Sample problem: Doppler effect

Variables

What is the strategy?

1. Use the equation for determining the Doppler effect when a sound-emitting object is moving toward a listener.


2. Then use the equation for determining the Doppler effect when a sound-emitting object is moving away from a listener.

Physics principles and equations

The equation for a sound source approaching a listener

The equation for a sound source moving away from a listener

Step-by-step solution

We start by calculating the frequency perceived by the front listener. The train is approaching that listener.

Now we calculate the frequency perceived by the rear listener, for whom the train is moving away.

This is quite a noticeable Doppler effect. The listener on the right hears a frequency roughly one-third higher than the listener on the left. If the

train were playing a musical note, the listener on the right would hear a pitch about five semitones (piano keys) higher than the listener on the

left.

The frequency of the train whistle

when the train is not moving is 495

Hz. What sound frequency does each

person hear?

speed of train vs= 50.0 m/s

speed of sound v = 343 m/s

frequency of train whistle when

train is motionless

fs= 495 Hz

frequency heard by front listener fL1

frequency heard by rear listener fL2

Step Reason

1. Doppler equation

2. substitute values

3. fL1 = 579 Hz evaluate

Step Reason

4. Doppler equation

5. substitute values

6. fL2 = 432 Hz evaluate

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