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:

The first overtone in a closed pipe has a frequency:

$A$ resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. $A$ tuning fork of frequency $512\,Hz$ produces the first resonance when the tube is filled with water to a mark $11\,cm$ below a reference mark,near the open end of the tube. The experiment is repeated with another fork of frequency $256\,Hz$,which produces the first resonance when water reaches a mark $27\,cm$ below the reference mark. The velocity of sound in air,obtained in the experiment,is close to .... $ms^{-1}$

In a resonance tube,the first resonance with a tuning fork occurs at $16 \ cm$ and the second at $49 \ cm$. If the velocity of sound is $330 \ m/s$,the frequency of the tuning fork is: (in $Hz$)

Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. The ratio of their lengths respectively is

The number of possible natural oscillations of an air column in a pipe closed at one end of length $85 \, cm$ whose frequencies lie below $1250 \, Hz$ are (Velocity of sound $= 340 \, m s^{-1}$)