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 cm and the density ratio of the gases is \({\rho }_{1}:{\rho }_{2}=1:16\), then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

Question

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 cm and the density ratio of the gases is \({\rho }_{1}:{\rho }_{2}=1:16\), then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

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