$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio:

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

An open pipe of length $l$ is vibrating in the $3^{rd}$ overtone with a maximum amplitude $A$. The amplitude at a distance of $\frac{l}{16}$ from any open end is

The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce $3$ beats. The length of open pipe is made $(\frac{1}{3})^{rd}$ and closed pipe is made $3$ times the original, the number of beats produced will be {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 $...........\,Hz$.

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 $\,cm$)