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 $s$)

$A$ 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 $Hz$)

It is possible to hear beats from two vibrating sources of frequency:

Two sitar strings $A$ and $B$ playing the note '$Ga$' are slightly out of tune and produce beats of frequency $6 \; Hz$. The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3 \; Hz$. If the original frequency of $A$ is $324 \; Hz$,what is the frequency (in $Hz$) of $B$?

$A$ tuning fork $A$ produces $4$ beats/sec with another tuning fork $B$ of frequency $320 \text{ Hz}$. On filing the fork $A$,$4$ beats/sec are again heard. The frequency of fork $A$ after filing is .... $\text{Hz}$

$A$ set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \; Hz$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first,then the frequency of the last fork is $\dots \; Hz$.