A detector is released from rest under gravity over a source of sound of frequency $f_{0} = 10^{3} H z$ . The frequency observed by the detector at time t is plotted in the graph. The speed of sound in air is $(g = 10 m / s e c^{2})$ (solve the problem by using apparent frequency relation, when the observer is moving with constant velocity)

310m/s

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300m/s

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350m/s

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330m/s

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Solution

The correct option is B
300m/s

$f = (\frac{V_{s} + V_{0}}{V_{s}}) f_{0} \Rightarrow f = (\frac{V_{s} + g t}{V_{s}}) f_{0} = f_{0} + \frac{g f_{0}}{V_{s}} t$

Slope from graph = $\frac{10^{3}}{30} = \frac{g f_{0}}{V_{s}}$

$\Rightarrow V_{s} = \frac{30}{10^{3}} g f_{0} = \frac{30}{10^{3}} \times 10 \times 10^{3} = 300 m / s$

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