A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is $340 m s^{- 1}$ , the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of $10 m s^{- 1}$ respectively are

500 Hz, 0.7 m

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500 Hz, 0.68 m

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486 Hz, 0.7 m

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515 Hz, 0.68 m

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Solution

The correct option is D 515 Hz, 0.68 m
Since the source of sound is stationary, the wavelength remains unchanged by the motion of the observer.
Therefore, $λ = \frac{v}{f} = \frac{340}{500} = 0.68 m$
The frequency of sound heard by the observer, $f^{'} = \frac{S p e e d o f s o u n d r e l a t i v e t o t h e o b s e r v e r}{W a v e l e n g t h}$
$= \frac{340 + 10}{0.68} = 514.7 ≃ 515 H z$
Hence, the correct choice is (d).

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A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is 340 ms−1, the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of 10 ms−1 respectively are

A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is $340 m s^{- 1}$ , the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of $10 m s^{- 1}$ respectively are