Question

A whistle S of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of largest and smallest frequency detected by a detector D at rest at a distance $2R$ from the centre of circle as shown in figure?
(take $c$ as speed of sound)

• A. $\left(\frac{c+v}{c-v}\right)$
• B. $\sqrt{2}\left(\frac{c+v}{c-v}\right)$
• C. $\sqrt{2}$
• D. $\frac{(c+v)}{c\sqrt{2}}$

Answer 1

The correct option is A

$\left(\frac{c+v}{c-v}\right)$

Largest frequency will be detected when the source approaches detector along the line joining and the smallest frequency will be detected when the source recedes the detector along the line joining them
$\frac{f_1}{f_2}=\frac{\left(\frac{c}{c-v}\right)f}{\left(\frac{c}{c+v}\right)f}=\frac{c+v}{c-v}$

Why this question? Caution: In the expression according to the doppler effect, $\nu =\frac{v+u_0}{v-u_s}{\nu }_0$, $u_s$ is the speed of the source with respect to the medium, considered positive when it moves towards the observer and negative when it moves away from the observer.