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 $f_1.$ An observer in the other vehicle hears the frequency of the whistle to be $f_2.$ The speed of sound in still air is $v.$ Which of the following is /are the correct statement(s)?

[Assume, $u>w$]

• 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, $f_2<f_1$.

Answer 1

Answer: (A), (B)

If the wind blows from the source to the observer, $f_2>f_1$.


Case -I:

When wind is blowing from observer to source,
$f_2=f_1\left(\frac{v-w\pm u}{v-w\mp u}\right)$

Since source and observer are moving towards each other, we can write that,
$f_2=f_1\left(\frac{v-w+u}{v-w-u}\right)$

which is greater than $f_1.$
[since $u>w$ is given]


Case -II:

When wind is blowing from source to observer

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

which is again greater than $f_1.$
[since $u>w$ is given]

Hence, options (a) and (b) are correct.