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:

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of the air columns in their $p^{\text{th}}$ overtone respectively is

$A$ gas is filled in an organ pipe and it is sounded in its fundamental mode. Choose the correct statement$(s)$ : ($T$ = constant)

An empty vessel is partially filled with water. What happens to the frequency of vibration of the air column in the vessel?

$A$ tube closed at one end and containing air is excited. It produces the fundamental note of frequency $512 \ Hz$. If the same tube is open at both ends,the fundamental frequency that can be produced is .... $Hz$.

$A$ resonance tube closed at one end is of height $1.5 \ m$. $A$ tuning fork of frequency $340 \ Hz$ is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is . (Neglect end correction,speed of sound in air $= 340 \ m/s$) (in $cm$)