A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \( \rho_1 \) and \( \rho_2 \), respectively. The frequency of \( 9^{\text{th}} \) harmonic of closed tube is identical with \( 4^{\text{th}} \) harmonic of open tube. If the length of the closed tube is \( 10 \, \text{cm} \) and the density ratio of the gases is \( \rho_1 : \rho_2 = 1 : 16 \), then the length of the open tube is:
