A source of sound and detector are arranged as shown in Fig. The detector is moving along a circle with constant angular speed `omega`. It start from the shown location in anticlockwise direction at `t=0`
(Take velocity of sound in air as v)
What is the frequency as received by detector, when it rotates by an angle `(pi)/(2)`?

Options

A. f
B. `(v-omegaR)/(v)xxf`
C. `(v-(omega)/( R))/(v)xxf`
D. `v-(omegaRxx(2)/(sqrt5))/(v)xxf`

Answer

D

Explanation

The location of detector at required instant is shown in Fig.
We have, `v_0=Romega`
`f_(ap)=(v-v_0costheta)/(v)xxf`
`costheta=(2R)/(sqrt(5)R)`
`f_(ap)=(v-omegaRxx(2)/(sqrt5))/(v)xxf`