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 f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is v. The correct statement(s) is (are)

Question

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 f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is v. The correct statement(s) is (are) (A) If the wind blows from the observer to the source, f2 > f1 (B) If the wind blows from the source to the observer, f2 > f1 (C) If the wind blows from the observer to the source, f2 < f1 (D) If the wind blows from the source to the observer, f2 < f1

Tardigrade Admin · Accepted Answer

When wind blows from S to O f2=f1((v+w+u/v+w-u)) or f2>f1 when wind blows from O to S f2 =f1((v-w+u/v-w-u)) ∴ f2 >f1

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 the observer to the source, $f_{2} < f_{1}$

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

When wind blows from $S$ to $O$
$f_{2} = f_{1} (\frac{v + w + u}{v + w - u})$
or $f_{2} > f_{1}$
when wind blows from $O$ to $S$
$f_{2} = f_{1} (\frac{v - w + u}{v - w - u})$
$∴ f_{2} > f_{1}$

If the wind blows from the observer to the source, f2​>f1​

If the wind blows from the source to the observer, f2​>f1​

If the wind blows from the observer to the source, f2​<f1​

If the wind blows from the source to the observer, f2​<f1​

When wind blows from S to O f2​=f1​(v+w−uv+w+u​) or f2​>f1​ when wind blows from O to S f2​=f1​(v−w−uv−w+u​) ∴f2​>f1​

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 the observer to the source, $f_{2} < f_{1}$

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

When wind blows from $S$ to $O$
$f_{2} = f_{1} (\frac{v + w + u}{v + w - u})$
or $f_{2} > f_{1}$
when wind blows from $O$ to $S$
$f_{2} = f_{1} (\frac{v - w + u}{v - w - u})$
$∴ f_{2} > f_{1}$