Two vehicles, each moving with speed $u$ on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity $w$ . One of these vehicles blows a whistle of frequency $f_{1}$ .An observer in the other vehicle hears the frequency of the whistle to be $f_{2}$ . The speed of sound in still air is $V$ . The correct statement(s) is (are)

If the wind blows from the observer to the source,

f_{2} > f_{1}

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If the wind blows from the source to the observer,

f_{2} > f_{1}

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If the wind blows from observer to the source,

f_{2} < f_{1}

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If the wind blows from the source to the observer

f_{2} < f_{1}

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Solution

The correct options are
A If the wind blows from the observer to the source, $f_{2} > f_{1}$
B If the wind blows from the source to the observer, $f_{2} > f_{1}$
If wind blows from source to observer
$f_{2} = f_{1} (\frac{V + w + u}{V + w - u})$

When wind blows from observer towards source
$f_{2} = f_{1} (\frac{V - w + u}{V - w - u})$

In both cases, $f_{2} > f_{1}$

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