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A fixed source of sound emitting a certain frequency $f_{0}$ . When an observer approaching the source with a velocity $v_{0}$ apparent frequency received by the observer is $f_{1}$ and when the observer is going away the frequency received by the observer is $f_{2}$ , then actual frequency $f_{0}$ is:

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$\frac{2 f_{1} f_{2}}{f_{1} + f_{2}}$

$\frac{f_{1} + f_{2}}{2}$

$\frac{f_{1} - f_{2}}{2}$

$\sqrt{f_{1} f_{2}}$

answer is A.

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Detailed Solution

when observer is approaching a stationary source apparent frequency is $f_{1} = (\frac{v + v_{0}}{v}) f_{0}$

and when it is receding away $f_{2} = (\frac{v - v_{0}}{v}) f_{0}$

$f_{1} = (1 + \frac{v_{0}}{v}) f_{o} f_{2} = (1 - \frac{v_{0}}{v}) f_{o}$

adding we get $f_{1} + f_{2} = 2 f_{o}$

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