First slide

Doppler

Question

A police car moving with velocity 22 m/s and emitting sound of frequency 176 Hz follows a motor-cyclist which in turn is moving towards a stationary car and away from the police car as shown in fig. [2).

The stationary car is emitting a sound of frequency 165 Hz. If motor-cyclist does not hear any beat, then his velocity is

Moderate

A

11 m/s
B

22 m/s
C

33 m/s
D

44 m/s

Solution

The frequency of police car heard by motor-cyclist
$n^{'} = (\frac{332 - v}{332 - 22}) \times 176 The hequency of stationari car heard by motor - cyclist n^{''} = (\frac{332 + v}{332}) \times 166 As no beat is heard by motor cyclist n^{'} = n^{''} (\frac{332 - V}{332 - 22}) \times 176 = (\frac{332 + V}{332}) \times 166 Solving, we get v = 22 m / s$

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