A train approaching a hill at a speed of `40 km//hr` sounds a whistle of frequency `580 Hz` when it is at a distance of `1km` from a hill. A wind with a speed of `40km//hr` is blowing in the direction of motion of the train Find
(i) the frequency of the whistle as heard by an observer on the hill,
(ii) the distance from the hill at which the echo from the hill is heard by the driver and its frequency.
(Velocity of sound in air `= 1, 200 km//hr`)

Answer

A, B, C

Explanation

(i) The frequency of the whistle as heard by observer on the hill
`n' = n[(v + v_(m))/(v + v_(m) - v_(s))]`
`=580[(1200 + 40)/(1200 + 40 - 40)] = 599 Hz`

(ii) Let echo from the hill is heard by the driver at `B` which is at a distance `x` from the hill.
The time taken by the driver to reach from `A to B`
`t_(1) = (1 - x)/(40)` ...(i)
The time taken by the echo to reach from hill
`t_(2) = t_(AH) + t_(HB)`
`t_(2) = (1)/((1200 + 40)) +(x)/ ((1200 - 40))` ....(ii)
where `t_(AH) = time taken by sound from `A` to `H` with velocity (1200 + 40)`
`t_(HB) = time taken by sound from `H` to `B` with velocity 1200 - 40`
From (i) and (ii)
`t_(1) = t_(2)` rArr `(1 - x)/(40) = (1)/(1200 + 40) + (x)/(1200 - 40)`
rArr `x = 0.935 km`
The frequency of echo as heard by the driver can be calculate by considering that the source is the acoustic image.
`n' = n[((v - v_(m)) + v_(s))/((v - v_(m)) - v_(0))]`
`=580[((1200 - 40) + 40)/((1200 - 40) - 40)] = 621 Hz`