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

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 \(\mathrm{V}=3 \mathrm{~V}_{1}\)
\(\Longrightarrow \frac{\mathrm{V}}{\mathrm{V}_{1}}=3\)