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Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows 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)

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If the wind blows from the observer to the source, $f_{2} > f_{1} .$

If the wind blows from the source to the observer, $f_{2} > f_{1} .$

If the wind blows from observer to the source, $f_{2} < f_{1} .$

If the wind blows from the source to the observer, $f_{2} < f_{1} .$

answer is A, B.

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Detailed Solution

If the wind blows from source to observer (as shown in the figure), the apparent frequency is

$f_{2} = [\frac{(V + w) - (- u)}{(V + w) - (+ u)}] f_{1} = (\frac{V + w + u}{V + w - u}) f_{1} \Rightarrow f_{2} > f_{1}$

If the wind blows from observer to sound,

$f_{2} = [\frac{(V - w) - (- u)}{V - w - (+ u)}] f_{1} = (\frac{V - w + u}{V - w - u}) f_{1} \Rightarrow f_{2} > f_{1}$

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