Physics - Sound Wave Question with Solution | TestHub

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, ${\mathrm{F}}_1={\mathrm{F}}_{\mathrm{o}}\left[\frac{{\mathrm{v}}_{\text{sound }}+{\mathrm{V}}_{\text{observer }}}{{\mathrm{v}}_{\text{sound }}}\right]$ $\mathrm{OR}{\mathrm{F}}_1={\mathrm{F}}_{\mathrm{o}}\left[\frac{\mathrm{V}+{\mathrm{V}}_1}{\mathrm{V}}\right]$ ...(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 $\mathrm{V}=3{\mathrm{V}}_1$ $⟹\frac{\mathrm{V}}{{\mathrm{V}}_1}=3$