Question

A source of sound and are arranged as shown in the figure. The detector is moving along a circle with constant angular speed $\omega$. It starts from shown location in anticlockwise direction at t = 0. Velocity of sound in air is V. The time at which the detector will hear the maximum frequency for the first time is $\frac{5\pi }{k\omega }$. Then the value of K is

• A. 3
• B. 6
• C. 2
• D. 4

Answer 1

The correct option is A

3

The location of detector at required instant is shown in the figure below. $V_0=R\omega$ The instants at which detector hears maximum and minimum frequencies are shown in the figure that follows. A corresponds to minimum frequency while B corresponds to maximum frequency.

$cos\theta =\frac{R}{2R}=\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}$

Let detector reaches at A in time $t_0$ ( measured from the starting instant )

$\theta =\omega t_0\Rightarrow \frac{\pi }{3}=\omega t_0\Rightarrow t_0=\frac{\pi }{3\omega }$

Let detector reaches at B in times $t_{01}$ ( measured from A )

$2\pi -2\theta =\omega \times t_{01}\Rightarrow t_{01}=\frac{4\pi }{3\omega }$

The time taken after which the detector hears the maximum frequency for the first time

$t_0+t_{01}=\frac{5\pi }{3\omega }$