A police car moving at 22 m s - 1 chases a motorcyclist. The policeman sounds his horn at 176 Hz , while both of them move towards a stationary siren of frequency 165 Hz . Calculate the speed of the m

Question

A police car moving at 22 m s - 1 chases a motorcyclist. The policeman 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 (speed of sound = 330 m s - 1 )

TestHub · Accepted Answer

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.

$f_{1} = f_{2}$

$∴ 176 (\frac{330 - v}{330 - 22}) = 165 (\frac{330 + v}{330})$

Solving this equation, we get $v = 22 {m s}^{- 1}$

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