Question

A source is moving in a circle of radius $3m$ with constant angular velocity $\omega =5\text{rad/s}$. If the observer is at a distance $5m$ from the centre of circle, the time interval between maximum and minimum frequency received by the observer is

• A. $\frac{\pi }{5}$
• B. $\frac{2}{5}co{s}^{-1}\left(\frac{3}{4}\right)$
• C. $\frac{2}{5}{\cos }^{-1}\left(\frac{3}{5}\right)$
• D. $\frac{2}{5}{\sin }^{-1}\left(\frac{3}{5}\right)$

Answer 1

The correct option is C $\frac{2}{5}{\cos }^{-1}\left(\frac{3}{5}\right)$


Maximum frequency will correspond to source position A as the direction of instantaneous speed of source and sound will be same at A and minimum frequency will correspond to source position B as the direction of source speed and sound will be opposite at B.

So, the time interval between A and B $=\frac{2\theta }{\omega }=\frac{2{\cos }^{-1}\left(\frac{3}{5}\right)}{5}$
$[\theta ={\cos }^{-1}(\frac{3}{5})]$