A train is moving on a straight track with speed `20 m cdot s^(-1)`, It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is ( speed of sound = 320 m `cdot s^(-1)`) close to

Options

A. `6%`
B. `12%`
C. `18%`
D. `24%`

Answer

B

Explanation

Velocity of the listener. `v_(0) = 0,`
Velocity of the train, `v_(s) = 20 m//s`
So, apparent frequency when the train moves towards the listener,
`n_(2) = v/(v-(-v_(s)))=320/(320+20) xx1000 = 941.2` HZ
Hence, percentage change in the apparent frequency
`=(n_(1)-n_(2))/nxx100 = (1066.7-941.2)/1000xx100`
`= 12. 55 % approx12 %`
The option (B) is correct.