Question

A Kundt's tube apparatus has a copper rod of length $1.0\text{m}$ clamped at $25\text{cm}$ from one of the ends. The tube contains air in which the speed of sound is $340\text{m/s}$. The powder collects in heaps seperated by a distance of $10.0\text{cm}$. Find the speed of sound waves in copper.

• A. $1700\text{m/s}$
• B. $3400\text{m/s}$
• C. $5100\text{m/s}$
• D. $2700\text{m/s}$

Answer 1

The correct option is A $1700\text{m/s}$

Given,
Length at which copper rod is clamped $l=25\text{cm}\text{or}0.25\text{m}$
and $4l={\lambda }_{rod}=$ wavelength of sound wave in the rod

Seperation between the heaps $\left(\Delta l\right)=\frac{{\lambda }_{air}}{2}=10\text{cm}$

In a Kundt's tube experiment, rod behaves as an open organ pipe.
Since the frequency of vibration of rod and air are same, we can write that,

$\frac{v_{rod}}{v_{air}}=\frac{{\lambda }_{rod}}{{\lambda }_{air}}=\frac{2l}{\Delta l}$

$\Rightarrow v_{rod}=\frac{2l}{\Delta l}\times v_{air}$

Substituting the given values, we get

$v_{rod}=\frac{2\times 0.25}{0.1}\times 340=1700\text{m/s}$

Thus, option (a) is the correct answer.