Question

A source of frequency $f_0$ is moving on a circular path of radius R at constant speed of 10 m/s. At distance 2R from center of circular path is placed a detector. Frequency received by detector is $f$. Then,
(take speed of sound as 330 m/s)

• A. maximum value of $f$ is $\frac{33}{32}{f}_0$.
• B. maximum value of $f$ is less than $\frac{33}{32}{f}_0$.
• C. time interval between receiving maximum and minimum frequency is $\frac{\pi R}{15}$.
• D. time interval between receiving maximum and minimum frequency is $\frac{2\pi R}{15}$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A maximum value of $f$ is $\frac{33}{32}{f}_0$.
C time interval between receiving maximum and minimum frequency is $\frac{\pi R}{15}$.
D time interval between receiving maximum and minimum frequency is $\frac{2\pi R}{15}$.

$\sin \left(\theta \right)=\frac{R}{2R}\Rightarrow \theta ={30}^{\circ }and\alpha ={60}^{\circ }{f}_{max}=f_0\left(\frac{330}{330-10}\right)=\frac{33}{32}{f}_{0}Byt=\frac{\left(angletravelled\right)R}{v}{t}_1=\frac{2\pi R}{3\times 10}=\frac{\pi R}{15}and{t}_2=\frac{(2\pi -2\alpha )R}{v}=\frac{4\pi R}{3v}=\frac{2\pi R}{15}$