Question

The wave length ($\lambda$) of a sound and its frequency ($\eta$) are in inverse proportion to each other. The frequency is 320 Hertz when the wave length is 100 cm. Find the wave length of sound whose frequency is 400 Hertz.

Answer 1

$$\begin{gathered} \lambda \alpha \frac{1}{\eta }\left(\mathrm{Given}\right) \\ \therefore \lambda \eta =k\left(k\mathrm{is}\mathrm{a}\mathrm{constant}.\right) \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ 100\times 320=k\left(\eta =320\mathrm{Hz}\mathrm{when}\lambda =100\mathrm{cm}.\right) \\ \Rightarrow k=32000 \\ \therefore \lambda \eta =32000\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \mathrm{Now}, \\ \lambda \times 400=32000\left(\eta =400\mathrm{Hz}\right) \\ \lambda =\frac{32000}{400} \\ \therefore \lambda =80\mathrm{cm} \end{gathered}$$