$A$ light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 \, cm$,the frequency of the tuning fork is .... $Hz$

$A$ tuning fork arrangement (pair) produces $4 \, beats/sec$ with one fork of frequency $288 \, cps$. $A$ little wax is placed on the unknown fork and it then produces $2 \, beats/sec$. The frequency of the unknown fork is .... $cps$.

The displacement at a point due to two waves are $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$. The result due to their superposition will be

The air columns in two tubes closed at one end vibrating in their fundamental modes produce $2$ beats per second. The number of beats produced per second when the same tubes are vibrated in their fundamental mode with their both ends open are

$A$ source of frequency $\nu$ gives $6 \text{ beats/second}$ when sounded with a source of frequency $200 \text{ Hz}$. The second harmonic of frequency $2\nu$ of the source gives $8 \text{ beats/second}$ when sounded with a source of frequency $420 \text{ Hz}$. The value of $\nu$ is (in $text{ Hz}$)

Two tuning forks of frequencies $256 \ Hz$ and $258 \ Hz$ are sounded together. The time interval between two consecutive maxima is (in $s$)