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In the figure shown, a source of sound of frequency 510 Hz moves with constant velocity v_s = 20 m/s in the direction shown. The wind is blowing at a constant velocity v_w = 20 m/s towards an observer who is at rest at point B. Corresponding to the sound emitted by the source at initial position A, the frequency detected by the observer is equal to (speed of sound relative to air is 330 m/s)

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500 Hz

510 Hz

525 Hz

550 Hz

answer is C.

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Detailed Solution

Apparent frequency is given by

$\begin{matrix} n^{'} = n \frac{(u + v_{w})}{(u + v_{w} - v_{s} \cos 60^{\circ})} \\ = \frac{510 (330 + 20)}{330 + 20 - 20 \cos 60^{\circ}} \\ = 510 \times \frac{350}{340} = 525 Hz \end{matrix}$

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