Question

A whistle revolves in a circle with angular velocity $\omega =20rad/s$ using a string of length $50cm$. If the actual frequency of sound from the whistle is $385Hz$, then the minimum frequency heard by the observer far away from the centre is (velocity of sound $v=340m/s$)

• A. $385Hz$
• B. $374Hz$
• C. $394Hz$
• D. $333Hz$

Answer 1

The correct option is B $374Hz$

The diagram shows the velocities of the source at different points along its circular path.


There will be no change in frequency heard by the observer at points $B$ and $D$ since the velocity of the source line joining the source and observer.

$v_{source}=\omega \ast r=20\ast 0.5=10m/s$

At point $A$, there will be an increase in frequency

Minimum frequency will be heard at point $C$ since source is moving away from observer.

$f_C=f_0\left(\frac{v_{wave}}{v_{wave}+v_{source}}\right)$

$=385\left(\frac{340}{340+10}\right)=374Hz$