An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic).

• A
  $\frac{1}{3}$
• B
  $3$
• C
  $\frac{1}{6} \sqrt{\frac{\rho_1}{\rho_2}}$
• D
  $\frac{1}{6} \sqrt{\frac{\rho_2}{\rho_1}}$