a train standing at the outer signal of the railway station blows a whistle of frequency 400Hz in still air. what is the frequency of the whistle for a platform observer when the train:
(A) approaches the platform with a speed of 10m/s
(B) recedes from the platform with a speed of 10m/s.
(take the speed of sound in still air = 340m/s)

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Solution

We know
$f = \frac{v + v_{r}}{v + v_{s}} f_{o} W h e r e f_{o} f r e q u e n c y o f s o u r c e, v = v e l o c i t y o f s o u n d v_{r} = v e l o c i t y o f r e c i v e r v_{s} = v e l o c i t y o f s o u r c e .$
(a) Here given
$f_{o} = 400 H z, V_{r} = 0, v_{s} = - 10 m / s a n d v = 340 m / s$
Therefor
$f = \frac{340 + 0}{340 - 10} \times 400 H z = 412 H z$
Hence required frequency is 412 Hz

(b) Here given
$f_{o} = 400 H z, V_{r} = 0, v_{s} = + 10 m / s a n d v = 340 m / s$
Therefor
$f = \frac{340 + 0}{340 + 10} \times 400 H z = 388.57 H z$
Hence required frequency is 388.57Hz

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