Problem

Beats.jpg

A man standing at a bus stop when two cyclists travelling in the same direction toward him are each blasting a radio with sound of a single frequency. Each cyclist is travelling at 5 m/s. As the first cyclist passes him but before the second cyclist does, the man hears a beat frequency of 5 Hz.

What is the frequency of the sound played by the cyclists?

Use the speed of sound of 343 m/s in air.

Solution

This problem involves beat frequencies and Doppler shift. The formula for beat frequency is :.

Let the frequency from the second cyclist (as heard by the man) be , and the frequency from the first cyclist (as heard by the man) be .

Since the man is not moving, the beat frequency must be

.

Solving for the original frequency from the radio,

.

Thus


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