A closed organ pipe of length $L_{1}$ and an open organ pipe contain diatomic gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)
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Logic Tip: The first overtone of a closed pipe is the 3rd harmonic, while for an open pipe, it is the 2nd harmonic (which has frequency $v/L$).