The frequencies of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of tuning fork $C$. When $A$ and $B$ are simultaneously excited,$5$ beats per second are produced. Then the frequency of the tuning fork $A$ (in $Hz$) is

$A$ wire vibrates at a fundamental frequency of $500 \,Hz$. $A$ second identical wire produces $5$ beats per second with it when the tension in the first wire is slightly decreased. The ratio of the tension in the second wire to the tension in the first wire is approximately equal to

$5\, \text{beats/second}$ are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95\, \text{m}$ or $1\, \text{m}$. The frequency of the fork will be ... $\text{Hz}$.

$50$ tuning forks are arranged in increasing order of their frequencies such that each gives $4 \, \text{beats/sec}$ with its previous tuning fork. If the frequency of the last fork is the octave of the first, then the frequency of the first tuning fork is ... $Hz$.

$56$ tuning forks are arranged such that each fork produces $4$ beats per second with its previous one. If the frequency of the last fork is twice that of the first, the frequency of the $19^{\text{th}}$ fork is . . . . . . (in $\text{Hz}$)

$A$ wire under tension $225 \ N$ produces $6$ beats per second when it is tuned with a tuning fork. When the tension changes to $256 \ N$,it is again tuned with the same tuning fork,and the number of beats remains unchanged. The frequency of the tuning fork will be: (in $Hz$)