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Listener and Source Moving

Two sirens si...

Question

Two sirens situated one kilometer apart are producing sound of frequency 330 Hz. An observer starts moving from one siren to the other with a speed of 2 m/s. If the speed of sound be 330m/s, the beat frequency heard by the observer is

A

8

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B

4

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C

6

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D

1

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Solution

The correct option is A 4
The frequency when a person is moving towards a source is, $f_{1} = (\frac{V + V_{o}}{V}) f$

The frequency when a person is moving away is, $f_{2} = (\frac{V - V_{o}}{V}) f$

Beats $= f_{1} - f_{2} = (\frac{2 V_{o}}{V}) f = \frac{2 \times 2}{330} 330 = 4 H z$

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