When the observer moves towards a stationary source with velocity $\mathrm{V}_{1}$, the apparent frequency…
When the observer moves towards a stationary source with velocity $\mathrm{V}_{1}$, the
apparent frequency of emitted note is $\mathrm{F}_{1}$. When observer moves away from the
source with velocity $\mathrm{V}_{1}$, the apparent frequency is $\mathrm{F}_{2}$. If $\mathrm{V}$ is the velocity of sound in
air and $\mathrm{F}_{1} / \mathrm{F}_{2}=2$ then $\mathrm{V} / \mathrm{V}_{1}$ is equal to
5
6
4
3
Solution
Let the original frequency of the source be $\mathrm{F}_{\mathrm{o}}$.
From Doppler effect, apparent frequency heard by observer when it moves towards stationary source,
$\mathrm{F}_{1}=\mathrm{F}_{\mathrm{o}}\left[\frac{\mathrm{v}_{\text {sound }}+\mathrm{V}_{\text {observer }}}{\mathrm{v}_{\text {sound }}}\right]$
$\operatorname{OR} \mathrm{F}_{1}=\mathrm{F}_{\mathrm{o}}\left[\frac{\mathrm{V}+\mathrm{V}_{1}}{\mathrm{~V}}\right]$ ...(1)
From Doppler effect, apparent frequency heard by observer when it moves away from stationary source,
$\mathrm{F}_{2}=\mathrm{F}_{\mathrm{o}}\left[\frac{\mathrm{v}_{\text {sound }}-\mathrm{V}_{\text {observer }}}{\mathrm{v}_{\text {sound }}}\right]$
OR $\mathrm{F}_{2}=\mathrm{F}_{\mathrm{o}}\left[\frac{\mathrm{V}-\mathrm{V}_{1}}{\mathrm{~V}}\right]$ ...(2)
Dividing (1) and (2) we get $\frac{\mathrm{F}_{1}}{\mathrm{~F}_{2}}=\frac{\mathrm{V}+\mathrm{V}_{1}}{\mathrm{~V}-\mathrm{V}_{1}}$
Or $2=\frac{\mathrm{V}+\mathrm{V}_{1}}{\mathrm{~V}-\mathrm{V}_{1}}$
Or $2 \mathrm{~V}-2 \mathrm{~V}_{1}=\mathrm{V}+\mathrm{V}_{1}$
Or $\mathrm{V}=3 \mathrm{~V}_{1}$
$\Longrightarrow \frac{\mathrm{V}}{\mathrm{V}_{1}}=3$