Question

A pipe of length $1.5m$ closed at one end is filled with gas and resonates in its fundamental mode with a tuning fork. Another open organ pipe of same dimensions filled with air resonates in its fundamental mode with the same tuning fork. If this experiment is performed at $30^{\circ }C$ , then the speed of sound at $0{}^{\circ }C$ in the same gas is (Speed of sound in air is $360m/s$ )

• A. $580m/s$
• B. $683m/s$
• C. $880m/s$
• D. $743m/s$

Answer 1

Answer: (B)

For open pipe $f=\frac{v}{2\ell }=\frac{360}{2\times 15}=120Hz$
For the closed at one end pipe, let the velocity of sound in gas at $30{}^{{}^{\circ }}C$ be $v^{{}^{\prime }}$
$f^{{}^{\prime }}=\frac{v^{{}^{\prime }}}{4\ell }=\frac{v^{{}^{\prime }}}{4\times 1.5}=\frac{v^{{}^{\prime }}}{6}$
Since same tuning fork is used frequency will be same and thus,
$f^{{}^{\prime }}=f\Rightarrow v^{{}^{\prime }}=720m/s$
Also
$v\propto \sqrt{T}\Rightarrow v=720\times \sqrt{\frac{273}{303}}=683m/s.$