Question

A Kundt's tube apparatus has a copper rod of length 1.0 m clamped at 25 cm from one of the ends. The tube contains air in which the speed of sound is 340 m s⁻¹. The powder collects in heaps separated by a distance of 5.0 cm. Find the speed of sound waves in copper.

Answer 1

Given:
Speed of sound in air $v_{air}$ = 340 ms⁻¹
Velocity of sound in Kundt^'s tube $v_{\mathrm{rod}}$ = ?
Length at which copper rod is clamped l = 25 cm = 25$\times {10}^{-2}\mathrm{m}$
Distance between the heaps $∆l$ = 5 cm = $5\times {10}^{-2}\mathrm{m}$

$$\begin{gathered} \frac{v_{\mathrm{rod}}}{v_{\mathrm{air}}}=\frac{2l}{∆l} \\ \Rightarrow v_{\mathrm{rod}}=\frac{2l}{∆l}\times v_{\mathrm{air}} \\ \mathrm{On}\mathrm{substituting}\mathrm{the}\mathrm{respective}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{above}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ {v}_{\mathrm{rod}}=\frac{340\times 25\times {10}^{-2}\times 2}{5\times {10}^{-2}} \\ \Rightarrow v_{\mathrm{rod}}=3400\mathrm{m}/\mathrm{s} \end{gathered}$$