In a resonance tube,the first and second resonances are obtained at depths $22.7 \,cm$ and $70.2 \,cm$ respectively. The third resonance will be obtained at a depth of: (in $\,cm$)

Two closed organ pipes,when sounded simultaneously,give $4$ beats per second. If the longer pipe has a length of $1 \ m$,then the length of the shorter pipe will be,... $cm$ $(v = 300 \ m/s)$.

When the air column of a resonance tube is vibrated together with a tuning fork,$3$ beats are heard per second,either the temperature of the air column is $51^{\circ} C$ or $16^{\circ} C$. The frequency of the tuning fork is (in $Hz$)

An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \, Hz$ if the length of the column in $cm$ is (velocity of sound $= 330 \, m/s$)

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).

$A$ closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho _1}$ and ${\rho _2}$ respectively. The compressibility of gases is equal in both the pipes. Both the pipes are vibrating in their first overtone with the same frequency. The length of the open organ pipe is