An observer standing on a railway crossing receives frequencies 2.2 kHz and 1.8 kHz when the tran approaches and recedes from the observer. Find the velocity of the train (speed of sound in air is 300 m/s).

Answer

30

Explanation

`f .= (f _(0) (v pm v _(0)))/( (v pm v _(s))) = (f _(0) (V))/( v pm v _(s))`
When approaches : `2.2 xx 10 ^(3) ...(i)`
`= (f _(0) (300))/( 300 - V _(s))`
When recedes `: 1. 8 xx 10 ^(3) = (f _(0) (300))/( 300 + V _(s)) ...(ii)`
Dividing () by (ii)
`(2.2 )/(1.8) = ( 300 + V _(s))/( 300 - V _(s)) implies (4)/(0.4) = (600)/(2 V _(s))`
`implies V _(s) = 30 ms ^(-1)`