A train standing at the outer signal of a railway station blows a whistle of frequency 400Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of `10 ms^(-1)`. (b) recedes from the platform with a speed of `10ms^(-1)` ? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as `340ms^(-1)`.

Explanation

According to formula,
`(f _(L))/(v + v_(L)) = (f _(S))/(v+ v _(S))`
Placing the respective vaues, according to sign convention we get,
`(f _(L))/(340 + 0) = (400)/( 340 -10) `
`therefore f _(L) = (340 xx 400)/(330) = 412.1 Hz`

According to formula,
`(f._(L))/(v + v _(L)) = (f _(S))/( v + v _(S))`
Placing the respective values,
`(f._(L))/(340+0) = (400)/(340+10)`
` therefore f ._(L) = (340 xx 400)/(350) = 388.6 Hz`