Question

A small source of sound moves on a circle as shown in the figure and an observer is standing on $O$. Let $n_1$, $n_2$ and $n_3$ be the frequencies heard when the source is at $A,B$ and $C$ respectively. Then

• A. $n_1>n_2>n_3$
• B. $n_2>n_1>n_3$
• C. $n_1=n_2>n_3$
• D. $n_2>n_3>n_1$

Answer 1

The correct option is D $n_2>n_3>n_1$


Let $n_1$, $n_2$ and $n_3$ be the frequencies heard when the source is at $A$,$B$ and $C$respectively and an observer is standing on $O$.

From Doppler effect the apparent frequency heard by the observer,
$n_1=n\left(\frac{v+v_0}{v\mp v_s}\right)$

$n=$ actual frequency of the sound,
$v=$ speed of sound in medium,
$v_0=$ speed of observer,
$v_s=$ speed of source,

At point $A$, source is moving away from observer, so the apparent frequency
$n_1=n\left(\frac{v}{v+v_s}\right)$

which is less than actual frequency $\left(n\right)$.
$n_1<n$

At point $B$, source is moving towards the observer, so the apparent frequency
$n_2=n\left(\frac{v}{v-v_s}\right)$

which is more than actual frequency $\left(n\right)$.
$n_2>n$

At point $C$, source is moving perpendicular to the observer, so the apparent frequency is little higher than actual frequency but less than point $B$.
$n_3=n$

Therefore, the combined result of these three statements are expressed as,

$n_2>n_3>n_1$

Final answer: (b)