The ratio of the frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe having the same length is

$A$ tuning fork of frequency $340 \, Hz$ is sounded above an organ pipe of length $120 \, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \, m/s$)

$A$ string of length $3 \ m$ and linear mass density $0.0025 \ kg/m$ is fixed at both ends. One of its resonance frequencies is $252 \ Hz$. The next higher resonance frequency is $336 \ Hz$. Then the fundamental frequency will be ..... $Hz$.

$A$ closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x$ $(x << l)$,both in their fundamental mode. If $v$ is the speed of sound,the beat frequency heard is:

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length $L$. The length of the open pipe will be

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)