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Q.

A police car moving at $22 m / s$ , chases a motorcyclist. The police man sounds his horn at $176 H z$ . While both of them move towards a stationary siren of frequency $165 H z$ . Calculate the speed of the motorcyclist, if it is given that he does not observes any beats(Speed of sound $330 m / s$ ). nearly

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a

$33 m / s$

b

$22 m / s$

c

Zero

d

$11 m / s$

answer is B.

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Detailed Solution

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$\begin{array}{l} f_{1} = f r e q u e n c y o f t h e p o l i c e c a r h e a r d b y m o t o r c y c l i s t \\ f_{2} = f r e q u e n c y o f t h e s i r e n h e a r d b y m o t o r c y c l i s t \\ f_{1} = \frac{330 - v}{330 - 22} \times 176; f_{2} = \frac{330 + v}{330} \times 165 \\ f_{1} - f_{2} = 0 \Rightarrow v = 22 m / s \end{array}$

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