Question

A train approaching a hill at a speed of 40 km/h sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from the hill. A wind with a speed of 40 km/h 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 is 1200 km/h]

Answer 1

(i) The apparent frequency is

(ii) Let the driver be at O′ at a distance of x km from the hill when he hears the echo (Fig. 9.5). Time taken by the train to reach the point O′ from O is

Time taken by the sound to reach the point O′ from O after reflection at the hill is

For finding the frequency f ′′ as received by the driver we apply Doppler equation twice, first with the hill as observer (f ′) and then the hill as the source (see problem 12). Thus, we have