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. 0.12
B. 0.18
C. 0.24
D. 0.06

Answer

A

Explanation

`upsilon_(s) = 20` m/s. Whistle at the frequency of `f_(0) = 1000` Hz.
A person is standing near the track.
As the train approaches him, the frequency of the whislte as heard by him is
`f_(1) = ((upsilon - upsilon_(L))/(upsilon - upsilon_(s)))f_(0)`
(where `upsilon` = 320 m/s is the speed of sound in air)
`therefore" "f_(1) = 1000 xx ((320 - 0)/(320 - 20))`
`= 1000 xx (320)/(300)`
= 1066.67 Hz
As the train goes away from him, the frequency of the whistle as heard by him is
`f_(2) = ((upsilon - upsilon_(L))/(upsilon + upsilon_(s)))`
`f_(2) = 1000 xx ((320 - 0)/(320 + 20)) = 1000 xx (320)/(340)`
= 941.17 Hz.
Percentage change in frequency heard by the person standing near the track as the train passes him
`(f_(1) - f_(2))/(f_(0)) xx 100 = ((1066.67 - 941.17)/(1000)) xx 100`
`= (125.5)/(10) = 12.55% ~~ 12%`