Question

A closed organ pipe, of length 1.2 m and filled with a gas, is resonated in its fundamental mode with a fork. Another open pipe of same length but filled with air resonates with the same fork. The room temperature is ${40}^{\circ }C$. If the speed of sound in air at ${40}^{\circ }C$ is $360m{s}^{-1}$, then the speed of sound in gas at ${40}^{\circ }C$ will be

• A. $341.5m{s}^{-1}$
• B. $637m{s}^{-1}$
• C. $633m{s}^{-1}$
• D. $720m{s}^{-1}$

Answer 1

The correct option is D $720m{s}^{-1}$

Let velocity of sound in gas be $v_g$

Length of the pipe $L=1.2m$

Velocity of sound in air $v_s=360m/s$

Closed organ pipe with gas: Fundamental frequency ${\nu }_1^{\prime }=\frac{v_g}{4L}$

Open organ pipe with air : Fundamental frequency ${\nu }_1=\frac{v_s}{2L}$

But ${\nu }_1^{\prime }={\nu }_1$

$\frac{v_g}{4L}=\frac{v_s}{2L}⟹v_g=2v_s=2\times 360$

Thus $v_g=720m/s$