Two wires are in unison. If the tension in one of the wires is increased by $2\%$,$5$ beats are produced per second. The initial frequency of each wire is .... $Hz$.

$A$ tuning fork whose frequency as given by the manufacturer is $512 \ Hz$ is being tested with an accurate oscillator. It is found that the fork produces a beat of $2 \ Hz$ when the oscillator reads $514 \ Hz$,but produces a beat of $6 \ Hz$ when the oscillator reads $510 \ Hz$. The actual frequency of the fork is ..... $Hz$.

When temperature increases,the frequency of a tuning fork

Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously with tensions $T_1$ and $T_2$ respectively. On changing the tension slightly in one of them,the beat frequency remains unchanged. This will happen when (Given $\rightarrow T_1 > T_2$)

$A$ tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was .... $Hz$

What is a beat? Obtain the equation for the number of beats produced in unit time.