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

$A$ 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 $Hz$.

Two tuning forks $A$ and $B$ produce notes of frequencies $256 \ Hz$ and $262 \ Hz$ respectively. An unknown note sounded at the same time as $A$ produces beats. When the same note is sounded with $B$,the beat frequency is twice as large. The unknown frequency could be ... $Hz$

When two tuning forks (fork $1$ and fork $2$) are sounded together,$4$ beats per second are heard. Now some tape is attached to the prong of fork $2$. When the tuning forks are sounded again,$6$ beats per second are heard. If the frequency of fork $1$ is $200 \,Hz$,then the original frequency of fork $2$ is ........... $Hz$.

Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t$. The number of beats produced per minute is

Two sound waves of wavelengths $5 \ m$ and $6 \ m$ produce $30$ beats in $3 \ s$. The velocity of sound is .... $m/s$.