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 $Hz$)

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously,$4$ 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 what was the original frequency of fork $2$ (in $, Hz$)?

$A$ tuning fork gives $5$ beats with another tuning fork of frequency $100\,Hz.$ When the first tuning fork is loaded with wax,the number of beats remains unchanged. What is the frequency of the first tuning fork in $Hz$?

Three sound waves of equal amplitudes have frequencies $(n - 1)$,$n$,and $(n + 1)$. They superimpose to produce beats. The number of beats produced per second is:

Two tuning forks $A$ and $B$ produce notes of frequencies $258 \,Hz$ and $262 \,Hz$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is (in $\,Hz$)

The wavelengths of two notes in air are $\frac{36}{195} \,m$ and $\frac{36}{193} \,m$. Each note produces $10$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is