Two closed organ pipes having lengths $20\,cm$ and $20.5\,cm$ produce $5\,beats/sec$. Determine the frequency of both organ pipes.

$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):

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 $= 330 \, m/s$)

In the case of a closed organ pipe,which harmonic is the $p^{th}$ overtone?

If $l_1$ and $l_2$ are the lengths of the air column for the first and second resonance when a tuning fork of frequency $n$ is sounded on a resonance tube,then the distance of the displacement antinode from the top end of the resonance tube is:

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic)