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).

Explanation

`{:(rarr v_(s),,rarr v_(o) = 0),(overset(*)(S),,overset(*)(O)),(,rarrv,):}`
When source is moving towards observer, frequency received by stationary observer
`f_(1) = f((v)/(v - v_(s)))` (i)
`{:(rarr v_(s)=0,,rarr v_(o)),(overset(*)(S),,overset(*)(O)),(,rarrv,):}`
When source is moving away from observer, frequency received by stationary observer
`f_(2) = f((v)/(v + v_(s)))` (ii)
`(f_(1))/(f_(2)) = (v + v_(s))/(v - v_(s))`
`(2.2)/(1.8) = (v + v_(s))/(v - v_(s))`
`2.2 v - 2.2 v_(s) = 1.8 v + 1.8 v_(s)`
`0.4 v = 4 v_(s)`
`v_(s) = 0.1 v = 0.1 xx 300 = 30 m//s`