Question

A whistle revolves in a circle with a constant angular speed of $20\text{rad/s}$ connected with a string of length $50\text{cm}$. If the frequency of the sound from the whistle is $385\text{Hz}$, then what is the minimum frequency heard by an observer at rest who is far away from the centre?
(velocity of sound is $370\text{m/s}$)

• A. $385\text{Hz}$
• B. $375\text{Hz}$
• C. $394\text{Hz}$
• D. $333\text{Hz}$

Answer 1

The correct option is B $375\text{Hz}$

Given:
Angular speed of the whistle, $\omega =20\text{rad/s}$
Radius of the circle, $r=50\text{cm}=0.5\text{m}$
Frequency of sound from the whistle, $f=385\text{Hz}$
Velocity of sound, $v=370\text{m/s}$

The line joining the source and the observer will be a secant passing through the centre.

Frequency heard by observer will be minimum when the source recedes away from him as shown in above figure.
Speed of the source,
$v_s=r\omega =0.5\times 20=10\text{m/s}$
Now, frequency heard by the observer,
$\Rightarrow f_{min}=f_0\left(\frac{v}{v+v_s}\right)$
$\Rightarrow f_{min}=385\times \left(\frac{370}{370+10}\right)$
$\Rightarrow f_{min}=375\text{Hz}$