The first overtone frequency of a closed pipe of length $l_{1}$ is equal to the $2^{\text{nd}}$ harmonic frequency of an open pipe of length $l_{2}$. The ratio $\frac{l_{1}}{l_{2}}$ is:

If the end correction of an open pipe is $0.8 \ cm$,then the inner radius of that pipe will be

Two open organ pipes give $4$ beats/sec when sounded together in their fundamental modes. If the lengths of the pipes are $100 \ cm$ and $102.5 \ cm$ respectively,then the velocity of sound is ..... $m/s$.

If the lengths of the open and closed pipes are in the ratio of $2 : 3$, then the ratio of the frequencies of the third harmonic of the open pipe and the fifth harmonic of the closed pipe 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)

In a resonance tube of length $0.8 \,m$, an air column vibrates with a source of frequency $375 \,Hz$ for a certain height of water from the bottom of the tube. What is the water level corresponding to the fundamental frequency (in $\,m$)? (Neglect end correction, speed of sound in air = $330 \,m/s$)