Question

A closed organ pipe of length L and an open organ pipe contain gases of densities $p_1$ and $p_2$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Frequency of first over tone of closed pipe =

Frequency of first over tone of open pipe

$\Rightarrow \frac{3v}{4L_1}=\frac{v}{L_2}\Rightarrow \frac{3}{4L_1}\sqrt{\frac{\gamma P}{{\rho }_1}}=\frac{1}{L_2}\sqrt{\frac{\gamma P}{{\rho }_2}}[\therefore v=\sqrt{\frac{\gamma P}{\rho }}]$

$\Rightarrow L_2=\frac{4L_1}{3}\sqrt{\frac{{\rho }_1}{{\rho }_2}}=\frac{4L}{3}\sqrt{\frac{{\rho }_1}{{\rho }_2}}$