Two vehicles, each moving with speed u on the same horizontal str… - Vidyadip

MCQ

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) :

$(A)$ 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, $f_2 > f_1$.

$(C)$ If the wind blows from the observer to the source, $f _2 < f _1$.

$(D)$ If the wind blows from the source to the observer, $f _2 < f _1$.

A
$(A,C)$
✓
$(A,B)$
C
$(B,D)$
D
$(C,D)$

✓

Answer

Correct option: B.

$(A,B)$

b
$Image$

If wind blows from source to observer

$f_2 =\left(\frac{(v+w)+u}{(v+w)-u}\right) f_1 $

$\Rightarrow \quad f_2 > f_1$

If wind blows from observer to source

$Image$

$f_2=\left(\frac{(v-w)+u}{(v-w)-u}\right) f_1 $

$\Rightarrow f_2>f_1$

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