# 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 $340\: m\: s^{-1}$

Speed of the wind v= 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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