$A$ 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 .... $Hz$

Two tuning forks have frequencies $450\, Hz$ and $454\, Hz$ respectively. On sounding these forks together,the time interval between successive maximum intensities will be .... $sec$

Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6$ beats per second when both wires vibrate simultaneously?

Two tuning forks $F_1$ and $F_2$ produce $6$ beats per second when sounded together. The frequency of $F_1$ is $256 \ Hz$. When wax is applied to $F_2$,the number of beats per second remains $6$. What is the frequency of $F_2$ in $Hz$?

The lengths of the two pipes open at both ends are $L$ and $(L + L_1)$. If they are sounded together, the beat frequency will be ($v$ = velocity of sound in air)

Two sitar strings $A$ and $B$ playing the note $Sa$ are slightly out of tune and produce beats of frequency $5 \ Hz$. The tension of the string $B$ is slightly decreased and the beat frequency is found to decrease to $3 \ Hz$. What is the original frequency of $B$,if the frequency of $A$ is $255 \ Hz$?