$25$ tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce $3 \, Hz$ beats. If the frequency of the first tuning fork is the octave of the last fork,then the frequency of the $21^{st}$ fork is .... $Hz$

Two stretched strings $A$ and $B$ when vibrated together produce $4$ beats per second. If the tension applied to the string $A$ is increased,the number of beats produced per second increases to $7$. If the frequency of string $B$ is $480 \ Hz$ initially,what is the frequency of string $A$ (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 $......... \, Hz$.

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)

If two tuning forks $A$ and $B$ are sounded together,they produce $4$ beats per second. $A$ is then slightly loaded with wax,and they produce $2$ beats when sounded again. The frequency of $A$ is $256 \ Hz$. The frequency of $B$ will be: (in $Hz$)

Two waves of wavelengths $99\, cm$ and $100\, cm$ both travelling with velocity $396\, m/s$ are made to interfere. The number of beats produced by them per second is