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in Physics by (61.3k points)

A train approaching a hill at a speed of 40 km/hr. sounds its horn of frequency 580 Hz when it is at a distance of 1 km from the hill. A wind with a speed of 40 km/hr is blowing in the direction of motion of the train. Find

(a) The frequency of the horn as heard by the observer on the hill,

(b) 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.)

1 Answer

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As train is moving towards the stationary observer on the hill. And the wind is in direction of the motion of train, the frequency of the sound waves from horn heard to the observer on hill is given by n' = n [v'/v' - vs]

where v’ = v+w (sum of velocities of train and train). When this sound wave reflects from the hill, and travels towards the moving train, the frequency heard by the

driver is n' = n [v - w + vs/(v - w]

(a) The apparent frequency is given by 

n' = n [v + w/(v + w)vs]

V = 1200 km/hr., w = 40 km/hr., vs = 40 km/hr. and n = 580 Hz. 

n' = [1200 + 40/1200+40)-40] = 599.3Hz

(b) As shown in the figure, let the driver hear the echo when he is at a distance x km from the hill. Time taken by the train to reach the point B′ 

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