For a certain organ pipe, three successive resonance frequencies are observed at $425 \,Hz$, $595 \,Hz$, and $765 \,Hz$, respectively. The length of the pipe is (speed of sound in air $= 340 \,m/s$). (in $\,m$)

$A$ 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:

An open pipe is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency ${f_1}$. Now,it is closed at one end. If the frequency of the tuning fork is increased slowly from ${f_1}$,then again a resonance is obtained with a frequency ${f_2}$. If in this case the pipe vibrates in its $n^{th}$ harmonic,then:

$A$ pipe,$30.0 \; cm$ long,is open at both ends. Which harmonic mode of the pipe resonates a $1.1 \; kHz$ source? Will resonance with the same source be observed if one end of the pipe is closed? Take the speed of sound in air as $330 \; m s^{-1}$.

$A$ closed organ pipe of length $L_c$ and an open organ pipe of length $L_o$ contain different gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of the open organ pipe?

An organ pipe $P_1$,closed at one end,is vibrating in its first harmonic. Another pipe $P_2$,open at both ends,is vibrating in its third harmonic. Both are in resonance with a given tuning fork. The ratio of the lengths of $P_1$ and $P_2$ is: