$A$ source of frequency $\nu$ gives $6 \text{ beats/second}$ when sounded with a source of frequency $200 \text{ Hz}$. The second harmonic of frequency $2\nu$ of the source gives $8 \text{ beats/second}$ when sounded with a source of frequency $420 \text{ Hz}$. The value of $\nu$ is (in $text{ Hz}$)

Two vibrating strings $A$ and $B$ produce beats of frequency $8 \ Hz$. The beat frequency is found to reduce to $4 \ Hz$ if the tension in the string $A$ is slightly reduced. If the original frequency of $A$ is $320 \ Hz$, then the frequency of $B$ is: (in $Hz$)

Two tuning forks $X$ and $Y$ have frequencies $280 \,Hz$ and $284 \,Hz$. $A$ third tuning fork $Z$ has an unknown frequency. When $X$ and $Z$ are sounded together, a certain number of beats per second are heard. When $Y$ and $Z$ are sounded together, the beat frequency is found to be three times as great. The frequency of $Z$ is: (in $\,Hz$)

The string of a violin emits a note of $205 \,Hz$ at its correct tension. The string is tightened slightly and then it produces six beats in two seconds with a tuning fork of frequency $205 \,Hz$. The frequency of the note emitted by the taut string is .......... $Hz$.

Beats are produced by two waves given by $y_{1} = a \sin(2000 \pi t)$ and $y_{2} = a \sin(2008 \pi t)$. The number of beats heard per second is

When a tuning fork $A$ of unknown frequency is sounded with another tuning fork $B$ of frequency $256 \ Hz$,then $3$ beats per second are observed. After that,$A$ is loaded with wax and sounded again,and $3$ beats per second are observed. The frequency of the tuning fork $A$ is ..... $Hz$.