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 $\text{ Hz}$)

$16$ tuning forks are arranged in the order of increasing frequencies. Any two successive forks give $8$ beats per second when sounded together. If the frequency of the last fork is twice the first,then the frequency of the first fork is:

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 $Hz$)?

Two sitar strings,$A$ and $B$,playing the note $'Dha'$ are slightly out of tune and produce beats at a frequency of $5 \, Hz$. The tension of string $B$ is slightly increased and the beat frequency is found to decrease to $3 \, Hz$. If the frequency of $A$ is $425 \, Hz$,the original frequency of $B$ is ... $Hz$.

Two harmonic waves moving in the same direction superimpose to form a wave $x = a \cos(1.5 t) \cos(50.5 t)$ where $t$ is in seconds. Find the period with which they beat (close to the nearest integer). (in $s$)

$41$ tuning forks are arranged in increasing order of frequency such that each produces $5 \text{ beats/second}$ with the next tuning fork. If the frequency of the last tuning fork is double that of the frequency of the first fork,then the frequency of the first and last fork is: