In the fundamental mode,the time taken by the wave to reach the closed end of an air-filled pipe is $0.01 \ s$. The fundamental frequency is (in $Hz$)

For a certain organ pipe,the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of the fifth harmonic is $405 \, Hz$ and the speed of sound in air is $324 \, ms^{-1}$,the length of the organ pipe is $.......... m$.

An organ pipe of length $L$ is open at one end and closed at the other end. The wavelengths of the three lowest resonating frequencies that can be produced by this pipe are

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

$A$ 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 ..... $Hz$.

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)