Question

A small source of sound vibrating at a frequency $500Hz$ is rotated along a circle of radius $\frac{100}{\pi }$ cm at a constant angular speed of 5 revolutions per second. The minimum and maximum frequency of the sound observed by a listener situated in the plane of the circle is
(Speed of sound is $332m{s}^{-1}$)

• A. 338.5 Hz. 612.5 Hz
• B. 485.4 Hz. 535.6 Hz
• C. 435.3 Hz. 565.6 Hz
• D. 485.4 Hz. 515.5 Hz

Answer 1

Answer: (D)

The linear velocity of whistle, $v_s=r\omega$
$v_s=\frac{100}{\pi }cm\times 5rev/s$
$=\frac{1}{\pi }m\times 2\pi \times 5rev/s=10m/s$
When whistle approaches the listener, then the frequency of sound heard will be maximum and minimum.
$n_{\max }=n\left(\frac{v}{v-v_s}\right)=500\times \frac{332}{322}=515.5Hz$
$n_{\min }=n\left(\frac{v}{v+v_s}\right)=500\times \frac{332}{342}=485.4Hz$