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) $(\frac{c+v}{c-v})$(b) $\sqrt{2}(\frac{c+v}{c-v})$(c) √2(d) $\frac{(c+v)}{c\sqrt{2}}$

Answer 1

answer : option (a) $\left(\frac{c+v}{c-v}\right)$

Largest frequency will be detected when the source approaches detector along the line joining.

according to Doppler's effect,

e.g., largest frequency is given by,

$f_2=\left(\frac{c}{c-v}\right)f$

where v is speed of source (whistle )

c is speed of sound and f is initial frequency.

and the smallest frequency will be detected when the source recedes the detector along the line joining

according to Doppler's effect ,

e.g., smallest frequency is given by,

$f_1=\left(\frac{c}{c+v}\right)f$

now, ratio of largest and smallest frequency , $\frac{f_2}{f_1}=\left(\frac{c+v}{c-v}\right)$