Question

A source of sound is revolving in a circular orbit of a radius r with time period T. An observer is at a distance d from the circle. If the velocity of the sound is x, then the difference between the maximum & minimum frequencies received by this stationary observer (n is original frequency)

• A. $\frac{2\pi nr}{xT}$
• B. $\frac{2\pi rxn}{T}$
• C. $\frac{4\pi nr}{xT}$
• D. $\frac{4\pi nx}{rT}$

Answer 1

The correct option is C $\frac{4\pi nr}{xT}$

Highest frequency is when source is approaching and lowest when moving away.

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

$f_2=\left(\frac{v+v_o}{v}\right)f$

$f_1-f_2=\frac{2v_{o}f}{v}=\frac{2\phi }{x}{\left(\frac{2\pi }{T}\right)}^n$ $=\frac{4\pi \phi n}{x}[\because v=\phi \omega ]$