Question

A small source of sound moves on a circle as shown in fig. and an observer is sitting at $O$. Let at $v_1,v_2,v_3$ be the frequencies heard when the source is at $A,B$ and $C$ respectively.

• A. ${\upsilon }_1>{\upsilon }_2>{\upsilon }_3$
• B. ${\upsilon }_1={\upsilon }_2>{\upsilon }_3$
• C. ${\upsilon }_2>{\upsilon }_3>{\upsilon }_1$
• D. ${\upsilon }_1>{\upsilon }_3>{\upsilon }_2$

Answer 1

The correct option is C ${\upsilon }_2>{\upsilon }_3>{\upsilon }_1$

When the source is at $C$ the source speed is perpendicular to the line joining the observer and the source. Thus at this instant, the separation between the two is not changing and the frequency heard ${\nu }_3$ is same as the source. When the source is at $A$ the separation between them is increasing, so due to the Doppler effect $v_1<v_3$. But when the source is at $B$, the separation is decreasing and due to the Doppler effect $v_3<v_2$ So $v_2>v_3>v_1$.