An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \, Hz$ if the length of the column in $cm$ is (velocity of sound $= 330 \, m/s$)

$A$ closed organ pipe of length $L$ and an open organ pipe of length $L'$ contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of the gases is equal in both pipes. Both pipes are vibrating in their first overtone with the same frequency. The length of the open pipe is $L' = \frac{x}{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$,where $x$ is ......... . (Round off to the nearest integer)

When the air column of a resonance tube is vibrated together with a tuning fork,$3$ beats are heard per second,either the temperature of the air column is $51^{\circ} C$ or $16^{\circ} C$. The frequency of the tuning fork is (in $Hz$)

Obtain the equation for the frequency of a stationary wave produced in an open pipe and show that all harmonics are possible in it.

The fundamental frequency of an air column in pipe $A$ closed at one end is in unison with the second overtone of an air column in pipe $B$ open at both ends. The ratio of the length of the air column in pipe $A$ to that of the air column in pipe $B$ is:

Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series. The fundamental frequency of the new pipe so obtained will be