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A police car moving at 22 m/s chases a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that the motorcyclist does not observe any beats. (Velocity of sound = 330 m/s)

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33 m/s

22 m/s

zero

11 m/s

answer is B.

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Detailed Solution

from siren: $n_{1} = 165 [\frac{v + v_{m}}{v}]$
from police car: $n_{2} = 176 [\frac{v - v_{m}}{v - v_{s}}]$
$165 [\frac{v + v_{m}}{330}] = 176 [\frac{v - v_{m}}{308}]$

$165 [\frac{330 + v_{m}}{330}] = 176 [\frac{330 - v_{m}}{308}]$

$v_{m} = 22 {ms}^{- 1}$

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