$A$ 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 organ pipe filled with a gas at $27^{\circ}C$ resonates at $400\,Hz$ in its fundamental mode. If it is filled with the same gas at $90^{\circ}C$,the resonance frequency at the same mode will be $...........\,Hz$.

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is:

The $3^{\text{rd}}$ overtone of a closed organ pipe is in unison with the $3^{\text{rd}}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

The vibrations of four air columns are shown below. The ratio of frequencies 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: