Question

Police in a siren car moving with a velocity 20 ms^– chases a thief who is moving in a car with a velocity v₀ ms^-1. The police car sounds at frequency 300 Hz, and both of them move towards a stationary siren of frequency 400 Hz. Calculate the speed in which thief is moving. (Assume the thief does not observe any beat)

Answer 1

Velocity of sound v = 330 m/s

Velocity of a police siren car v_s = 20 m/s

Frequency of a police siren car f = 300 Hz

Let the velocity of the thief be v m/s

The frequency of police siren heard by a thief is

`"f"_1 = ((330 - "v")/(330 - 20)) xx 300`

`= ((330 - "v")/(310)) xx 300` Hz

Frequency of stationary siren = 400 Hz

Frequency of stationaiy siren heard by a thief

`"f"_2 = ((330 + "v")/(330)) xx 400`

If there are no beats then

f₁ = f₂

`((330 - "v")/(310)) xx 300 = ((330 + "v")/(330)) xx 400`

(330 - v) × 0.9677 = (330 + v) × 1.2121

330 × 0.2444 = 2.1798 v

`therefore "v" = (0.2444 xx 330)/2.1798`

= 36.99

= 37 m