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 ms^(-1)`
Velocity of car `(v_(s) )= 20 ms^(-1)`
Frequency of car (`f_1)= 300` Hz
Frequency of stationary siren (`f_(2)`)= 400 Hz
The speed of the thief (`v_(o)`)=?
`v_(1) = f_(1) [(v- v_(o))/(v - v_(s))]` and `v_(2) = f_(2) [ (v + v_(o))/(v)]`
Both are moving towards stationary siren `v_(1) = v_(2)`
`300 [(300 - v_(o))/(310) ] = 400 [(300 + v_(o))/(330)]`
`330 - v_(o) = (4 xx 310)/(3) [(330 + v_(o))/(330)]`
`330 - v_(o) = (1240)/(990) [330 + v_(o)] = 1.2525 (300 + v_(0))`
`330 - v_(o) = 413.325 + 1.2525 v_(o)`
`2.2525 v_(o) = -83.325`
`v_(o) = -36.99`
`therefore` Speed of the thief in moving = `36.99 ms^(-1)`