A police in a siren car moving with a velocity `20 ms^(-1)` chases a thief who is moving in a car with a velocity `v_(0)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.

Explanation

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 their be v m/s.
Frequency of police siren heard by thief is
`f_(1)=((330-v)/(330/20))xx300`
`=((330-v)/(310))xx300HZ`
Frequency of stationary sire `=400 HZ`
Freqeuncy of stationary siren heard by thief
`f_(2)=((330+v)/(330))xx400`
It there are no beats then
`f_(1)=f_(2)`
`((330-v)/(310))xx300=((330+v)/(330))xx400`
`(330-v)xx0.9677=(330+v)xx 1.2121`
`330xx0.2444=2.7198v`
`:.v=(0.2444xx330)/(2.1798)`
`=36.99`
`=37 m`