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):