$A$ string under a tension of $129.6 \ N$ produces $10 \ beats/s$ when it is vibrated along with a tuning fork. When the tension in the string is increased to $160 \ N$,it sounds in unison with the same tuning fork. Calculate the fundamental frequency of the tuning fork in $Hz$.

In a guitar,two strings $A$ and $B$ made of the same material are slightly out of tune and produce beats of frequency $6 \, Hz$. When the tension in $B$ is slightly decreased,the beat frequency increases to $7 \, Hz$. If the frequency of $A$ is $530 \, Hz$,the original frequency of $B$ will be $......... \, Hz$.

Ten tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce $4$ beats per second. The highest frequency is twice that of the lowest. Possible highest and lowest frequencies (in $Hz$) are ................

$A$ 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 $Hz$)?

Two sound waves having frequencies $250 \,Hz$ and $256 \,Hz$ superimpose to produce a beat wave. The resultant beat wave has intensity maximum at $t=0$. After how much time will an intensity minimum be produced at the same point?

$A$ set of $24$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \, Hz$ beats per second with the preceding one and the frequency of the last tuning fork is two times that of the first fork,find the frequency of the $5^{th}$ tuning fork in $Hz$.