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  • A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m s^-1.

Q.15.21 A train, standing in a station-yard, blows a whistle of frequency 400\: Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10\: m\: s^{-1}. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10\: m\: s^{-1} ?  The speed of sound in still air can be taken as 340\: m\: s^{-1}

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Speed of the wind vw = 10 m s-1

Speed of sound in still air va = 340 m s-1

Effective speed with which the wave reaches the observer = v = vw + va = 10 + 340= 350 m s-1

There is no relative motion between the observer and the source and therefore the frequency heard by the observer would not change.

The wavelength of the sound as heard by the observer is

\\\lambda =\frac{v}{\nu }\\ \lambda =\frac{350}{400}\\ \lambda =0.875m

The above situation is not identical to the case when the air is still and the observer runs towards the yard as then there will be relative motion between the observer and the source and the frequency observed by the observer would change.

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

The frequency as heard by the observer is

\\\nu _{o}=\frac{340+10}{340}\times 400\\ \nu _{o}=411.76Hz

\\\lambda=\frac{340}{400}\\ \lambda=0.85m

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Sayak

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