Question

A Kundt's tube apparatus has a copper rod of length $0.8\text{m}$ clamped at $40\text{cm}$ from one of the ends. The tube contains air in which the speed of sound is $330\text{m/s}$. The powder collected in the heaps are separated by a distance of $6\text{cm}$. What is the speed of sound wave in a copper rod?

• A. $8.8\text{km/s}$
• B. $3.4\text{km/s}$
• C. $4.4\text{km/s}$
• D. $6.8\text{km/s}$

Answer 1

The correct option is C $4.4\text{km/s}$

Given that,
Speed of sound in air $\left(v_g\right)=330\text{m/s}$
Length of rod $\left(l_r\right)=0.8m$
So wavelength ${\lambda }_r$ of sound in rod is
$\frac{\lambda r}{2}=0.8\Rightarrow {\lambda }_r=1.6m$
Distance between heaps $\left(l_g\right)=6cm=6\times {10}^{-2}m$
Wavelength ${\lambda }_g$ of sound in air is
$\therefore \frac{{\lambda }_g}{2}=6\times {10}^{-2}$
$\Rightarrow {\lambda }_g=12\times {10}^{-2}m$
as we know,
Frequency in rod $\left(f_r\right)=$ Frequency in air $\left(f_g\right)$
$\Rightarrow \frac{v_r}{{\lambda }_r}=\frac{v_g}{{\lambda }_g}$
$\Rightarrow v_r=\frac{{\lambda }_r}{{\lambda }_g}\times v_g=\frac{1.6}{12\times {10}^{-2}}\times 330=4400m/s=4.4km/s$