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 $\,cm$)

An air column,closed at one end and open at the other,resonates with a tuning fork when the smallest length of the column is $50\, cm$. The next larger length of the column resonating with the same tuning fork is .... $cm$.

In a physics lab,a student is performing an experiment with a resonance tube to find the speed of sound and its end correction. For this,he used a resonance tube of length $120 \ cm$. When the length of the air column in the tube is $16 \ cm$ and $50 \ cm$,he obtains the $I$ and $II$ resonance respectively,while a tuning fork of frequency $500 \ Hz$ is sounded just above the tube. Match the parameters in List-$I$ with their suitable values in List-$II$.

List-$I$	List-$II$
$A$. Wavelength of sound $(cm)$	$p$. $1$
$B$. Height of liquid column at $II$ resonance $(cm)$	$q$. $2$
$C$. Speed of sound $(m/s)$	$r$. $340$
$D$. End correction $(cm)$	$s$. $68$
$E$. Minimum level of liquid column at resonance $(cm)$	$t$. $70$

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

In fundamental mode,the time required for the sound wave to reach up to the closed end of a pipe filled with air is $t$ seconds. The frequency of vibration of the air column is

The lengths of two open organ pipes are $l$ and $(l + \Delta l)$ respectively. Neglecting end correction,the frequency of beats between them will be approximately (Here $v$ is the speed of sound).