A train is moving on a straight track with speed `20 ms^(-1).` It is blowing 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 close to (speed of sound = 320 `ms^(-1)).`

Options

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

Answer

B

Explanation

When train moves towards stationary listener,

`(f _(L))/( v + v _(L)) = (f _(S))/( v + v _(S))`
`therefore (f _(L))/( 320 + 0) = (1000)/(320 - 20) implies f _(L) = 1000 xx (320)/(300)`
`therefore f _(L) = 1067 Hz`
(ii) When train moves away from stationary listener

`(f ._(L))/( v + v _(L)) = (f _(S))/( v +v _(S))`
` therefore (f ._(L))/( 320 +0) = (1000)/( 320 + 20) implies f._(L) = 1000 xx (320)/(340) `
`therefore f._(L) = 941 Hz`
Percentage decrease in frequency of sound heard by listener,
`(f _(L)-f ._(L))/( f _(L)) xx 100 %= (1067 - 941)/( 10 67) xx 100 %`
`= 11. 8 % = 12%`