Question

A pipe of length $1.5 \, m$ 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 $360 \, m/s$ )

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

Answer 1

Answer: (B)

For open pipe $f=\frac{v}{2 \ell }=\frac{360}{2 \times 15}=120 \, Hz$
For the closed at one end pipe, let the velocity of sound in gas at $30 \,{}^{^\circ }C$ be $v^{'}$
$f^{'}=\frac{v^{'}}{4 \ell }=\frac{v^{'}}{4 \times 1 . 5}=\frac{v^{'}}{6}$
Since same tuning fork is used frequency will be same and thus,
$f^{'}=f\Rightarrow v^{'}=720 \, m/s$
Also
$v \propto \sqrt{T}\Rightarrow v=720\times \sqrt{\frac{273}{303}}=683 \, m/s.$