Question

A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius $\frac{100}{\pi }$ cm at a constant angular speed of 5.0 revolutions per second. A listener situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air $=332m{s}^{-1}$.

Answer 1

According to given data,

Radius of the circle $=\frac{100}{\pi }cm$

$=\frac{100}{\pi }\times {10}^{-2}m$

$=\left(\frac{1}{\pi }\right)$ metres

$\omega =5$ rev/sec

So the linear speed,

$v=\omega r=\frac{5}{\pi }=\left(1.59\right)$

So, Velocity of the source,

$V_s=1.59$ m/s

So, let at the position A, the observer will listen maximum andat the position B it will listen minimum frequency.

So apparent frequency at A

$=\left(\frac{332}{332-1.59}\right)\times 500\approx 515Hz$

So apparent frequency at B

$=\left(\frac{332}{332+159}\right)\times 500\approx 485Hz$