Question

Sound waves of length travel from medium in which it's velocity is v m/s into another medium in which if velocity is 3 v m/s. What is the wavelength of sound in the second medium?

Answer 1

We know Velocity (V) $\propto$Wavelength ($\lambda$)
$$\begin{gathered} \Rightarrow \frac{\mathrm{V}}{\mathrm{\lambda }}=\mathrm{constant} \\ \Rightarrow \frac{{\mathrm{V}}_1}{{\mathrm{\lambda }}_1}=\frac{{\mathrm{V}}_2}{{\mathrm{\lambda }}_2} \\ \frac{\mathrm{velocity}\mathrm{in}\mathrm{first}\mathrm{medium}}{\mathrm{Wavelength}\mathrm{in}\mathrm{first}\mathrm{medium}}=\frac{\mathrm{velocity}\mathrm{in}\mathrm{second}\mathrm{medium}}{\mathrm{Wavelength}\mathrm{in}\mathrm{secondmedium}} \\ \Rightarrow \frac{\mathrm{V}}{\mathrm{\lambda }}=\frac{3\mathrm{V}}{\mathrm{Wavelength}\mathrm{in}\mathrm{second}\mathrm{medium}} \\ \Rightarrow \mathrm{Wavelength}\mathrm{in}\mathrm{second}\mathrm{medium}=3\mathrm{\lambda } \end{gathered}$$