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Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency 660 Hz. A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. then, u equals

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2.5 m/s

15.0 m/s

5.5 m/s

10.0 m/s

answer is A.

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Detailed Solution

f=660 Hz, v=330 m/s

The frequency observed due to $S_{1}, f_{1} = f (\frac{v - u}{v})$

The frequency observed due to $S_{2}, f_{2} = f (\frac{v + u}{v})$

Beat frequency observed,

$\begin{array}{l} f_{2} - f_{1} = \frac{f}{v} [v + u - (v - u)] \\ 10 = f_{2} - f_{1} = \frac{f}{v} [2 u] \end{array}$

Hence, u=2.5 m/s

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