Wave Motion 4 Question 16
15. 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, $f _2<f _1$
Show Answer
Answer:
Correct Answer: 15. (a)
Solution:
- When wind blows from $S$ to $O$
$$ \begin{aligned} f _2 & =f _1\left(\frac{\stackrel{\rightharpoonup}{v+u}}{v+w-u}\right)^{f _2} \end{aligned} $$
or
$$ f _2>f _1 $$
when wind blows from $O$ to $S$
$$ \begin{aligned} & f _2=f _1\left(\frac{v-w+u}{v-w-u}\right) \\ \therefore \quad f _2 & >f _1 \end{aligned} $$
