$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now ..... $f$.

$A$ 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 the same frequency. The length of the open organ pipe is (Neglect end correction).

The frequency of the second overtone of an open pipe is equal to the frequency of the first overtone of a closed pipe. The ratio of the lengths of the open pipe to the closed pipe is

$A$ cylindrical tube open at both ends has a fundamental frequency '$f$' in air. The tube is dipped vertically in water so that half of its length is in water. The new fundamental frequency is

An open pipe of length $l$ is vibrating in the $3^{rd}$ overtone with a maximum amplitude $A$. The amplitude at a distance of $\frac{l}{16}$ from any open end is