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 )

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 ), 33 m s - 1, 22 m s - 1, Zero, 11 m s - 1

MARKS App · 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 ∴ 1 7 6 3 3 0 - v ⁡ 3 3 0 - 2 2 = 1 6 5 3 3 0 + v ⁡ 3 3 0 Solving this equation, we get v ⁡ = 2 2 m s - 1

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