The frequencies of two tuning forks $A$ and $B$ are $1.5 \%$ more and $2.5 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $12$ beats are produced in $1$ second. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)

For the formation of beats,two sound notes must have:

Two tuning forks $P$ and $Q$ are vibrated together. The number of beats produced are represented by the straight line $OA$ in the following graph. After loading $Q$ with wax,they are vibrated together again and the beats produced are represented by the line $OB$. If the frequency of $P$ is $341 \ Hz$,the frequency of $Q$ will be ... $Hz$.

$A$ prong of a vibrating tuning fork is in contact with the water surface. It produces concentric circular waves on the surface of the water. The distance between five consecutive crests is $0.8 \ m$ and the velocity of the wave on the water surface is $56 \ m/s$. The frequency of the tuning fork is: (in $Hz$)

$A$ tuning fork $A$,marked $512 \ Hz$,produces $5$ beats per second when sounded with another unmarked tuning fork $B$. If $A$ is loaded with wax,the number of beats is again $5$ per second. What is the frequency of the tuning fork $B$ when not loaded (in $Hz$)?

When a guitar string is sounded with a $440\, Hz$ tuning fork,a beat frequency of $5\, Hz$ is heard. If the experiment is repeated with a tuning fork of $437\, Hz$,the beat frequency is $8\, Hz$. The string frequency $(Hz)$ is