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Q.

A train approaching a hill a speed of 40km/hr sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from a hill. A wind with a speed of 40 km/hr is blowing in the direction of motion of the train. Find the frequency (in Hz) of the whistle as heard by an observer on the hill. (velocity of sound in air = 1200 km/hr)

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answer is 599.

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Detailed Solution

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According to Doppler’s effect, the apparent frequency when both source and observer move along the same direction is
$n^{'} = \frac{(v + w) - v_{0}}{(v + w) - v_{s}}$
Velocity of observer $v_{0} = 0 ∴ n^{'} = \frac{(v + w)}{v + w - v_{s}} n$
Given $v = 1200 k m / h r, w = 40 k m / h r, v_{s} = 40 k m / h r, a n d n = 580 H z$
$∴ n^{'} = \frac{1200 + 40}{(1200 + 40) - 40} \times 580 = 599.33 H z = 600 H z .$

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