# Q.15.20 A train, standing at the outer signal of a railway station blows a whistle of frequency $400 \: Hz$ in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of $10\: m\; s^{-1}$, (b) recedes from the platform with a speed of $10\: m\; s^{-1}$? (ii) What is the speed of sound in each case ? The speed of sound in still air can be taken as $340\: m\; s^{-1}$.

S Sayak

$\nu _{o}=\left ( \frac{v\pm v_{o}}{v\pm v_{s}} \right )\nu$

where $\\\nu _{o}$ is the frequency as observed by the observer, $\nu$ is the frequency of the source, v is the speed of the wave, vo is the speed of the observer and vis the speed of the source.

(i) (a) When the source is moving towards the observer and the observer is stationary.

$\\\nu _{o}=\left ( \frac{v}{v- v_{s}} \right )\nu \\ \nu _{o}=\frac{340}{340-10}\times 400\\ \nu _{o}=412Hz$

(b)

$\\\nu _{o}=\left ( \frac{v}{v+ v_{s}} \right )\nu \\ \nu _{o}=\frac{340}{340+10}\times 400\\ \nu _{o}=389Hz$

(ii) The speed of the sound does not change as it is independent of the speed of observer and source and remains equal to 340 m s-1.

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