Question

A closed organ pipe of length L and an open organ pipe contain gases of densities ${\rho }_1$ and ${\rho }_2$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their second overtone with same frequency. The length of the open organ pipe is

• A. $\frac{L}{3}$
• B. $\frac{4L}{3}$
• C. $\frac{6L}{5}\sqrt{\frac{{\rho }_1}{{\rho }_2}}$
• D. $\frac{5L}{6}\sqrt{\frac{{\rho }_2}{{\rho }_1}}$

Answer 1

The correct option is C $\frac{6L}{5}\sqrt{\frac{{\rho }_1}{{\rho }_2}}$

Frequency of first over tone of closed pipe = Frequency of second over tone of open pipe
$\Rightarrow \frac{5v}{4L_1}=\frac{3v}{2L_2}\Rightarrow \frac{5}{4L_1}\sqrt{\frac{\gamma P}{{\rho }_1}}=\frac{3}{2L_2}\sqrt{\frac{\gamma P}{{\rho }_2}}[\because v=\sqrt{\frac{\gamma P}{\rho }}]$