Two sound waves having displacements $x_1 = 2 \sin(1000 \pi t)$ and $x_2 = 3 \sin(1006 \pi t)$,when interfere,produce

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 identical wires are vibrating in unison. If the tension in one of the wires is increased by $2 \%$,five beats are produced per second by the two vibrating wires. The initial frequency of each wire is $(\sqrt{1.02} \approx 1.01)$. (in $Hz$)

$A$ tuning fork of frequency $100 \, Hz$ when sounded together with another tuning fork of unknown frequency produces $2$ beats per second. On loading the tuning fork whose frequency is not known and sounding it together with the tuning fork of frequency $100 \, Hz$,it produces one beat. The frequency of the other tuning fork is: (in $, Hz$)

The frequencies of two tuning forks $A$ and $B$ are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $10$ beats are produced in $1 \text{ s}$. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)

$A$ set of $28$ tuning forks is arranged in an increasing order of frequencies. Each fork produces '$x$' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the $12^{\text{th}}$ fork is $152 \text{ Hz}$,the value of '$x$' (number of beats per second) is: