A train is moving on a straight track with speed `20ms^(-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 ms^(-1)`) close to :

Options

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

Answer

B

Explanation

Here, `v=1000Hz, upsilon_(s)=20ms^(-1), upsilon=320ms^(-1)`
Frequency heard by a person standing near the track when the whistling train is apporaching him is
`v_(1)=(upsilon)/(upsilon-upsilon_(s))v=(320)/(320-20)xx100=(320)/(300)xx1000` …(i)
Frequency heard by a person when the whistling train has crossed him
`v_(2)=((upsilon)/(upsilon-upsilon_(s)))v=(32)/(320+20)xx1000=(320)/(340)xx1000`
`%` change in frequency
`=(v_(1)-v_(2))/(v_(1))xx100=(1-v_(2)/(v_(1)))xx100`
`=(1-(300)/(340))100~~12%`