In a resonance tube experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

$A$ tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27\,^{\circ}C$,two successive resonances are produced at $20\,cm$ and $73\,cm$ of column length. If the frequency of the tuning fork is $320\,Hz$,the velocity of sound in air at $27\,^{\circ}C$ is .... $m/s$.

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length $L$. The length of the open pipe will be

Two open organ pipes of length $25 \ cm$ and $25.5 \ cm$ produce $10 \ \text{beats/sec}$. The velocity of sound will be ..... $m/s$.

An open and a closed organ pipe have the same length. The ratio of the $p^{th}$ mode of frequency of vibration of the two pipes is

If $v$ is the speed of sound in air,then what is the shortest length of a closed pipe that resonates at a frequency $n$?