A stationary source emits sound of frequency $f_{0} = 492$ Hz. The sound is reflected by a large car approaching the source with a speed of $3 m s^{- 1}$ . The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz to the nearest integer? (Given that the speed of sound in air is $330 m s^{- 1}$ and the car reflects the sound at the frequency it has received).

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answer is 9.

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Detailed Solution

$f^{'} = f_{o} [\frac{v + v_{c}}{v - v_{c}}] = 492 [\frac{330 + 3}{330 - 3}] = 501 H z$
Original frequency $f_{0} = 492 H z$
Final frequency $f^{'} = 501 H z$
Beat frequency $= | f^{'} - f_{0} | = 9 H z$

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