A police car moving at `22 ms^(-1)` chases a motor cyclist. The police man sounds horn at 176 Hz. While both of them move towards a stationary siren of frequency 165 Hz. If the number of beats heard by the motor cyclist per second is zero, then the speed of motorcycle is (Speed of sound in air `= 330 ms^(-1)`)

Options

A. `33 ms^(-1)`
B. `22 ms^(-1)`
C. `44 ms^(-1)`
D. `11 ms^(-1)`

Answer

B

Explanation

According to the position, we draw the following situation,

Given, velocity of car, `v_(s_(1)) = 22 ms^(-1)`
speed of the sound in air, `v = 330 ms^(-1)`
apparent frequency of cyclist from the police car, `f_(1). = (v-v_(0))/(v-v_(s)) f_(1) rArr f_(1) f_(1). = (330 - v_(0))/(330 - 22) xx 176`
`= (330 - v_(0))/(308) xx 176`
apparent frequency by cyclist from the stationary siren,
`f._(2) = (v+v_(0))/(v) f_(2) = (330 + v_(0))/(330) xx 165`
Number of beats heard by the cyclist,
`n = f._(1) - f._(2) = 0` (Given, n = 0)
`f._(1) = f._(2)`
`rArr (330 - v_(0))(176)/(308) = (330 + v_(0))(165)/(330)`
`rArr v_(0) = 22 ms^(-1)`
`:.` Hence, the speed of motorcycle is `22 ms^(-1)`. So, the correct option is (b).