A train is moving on a straight track with speed `20 ms^(-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

`f_("before crossing") = f_(0)((c)/(c - v_(S))) = 1000((320)/(320 - 20))`
`f_("after crossing") = f_(0)((c)/(c + v_(S))) = 1000((320)/(320 + 20))`
`Deltaf = f_(0)"((2cv_(S))/(c^(2) - v_(S)^(2))) , (Deltaf)/(f) xx 100% = (2 xx 320 xx 20)/(300 xx 340) xx 100 = 12.54% approx 12%`