Two vibrating tuning forks produce progressive 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:

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

$A$ 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 $text{ Hz}$)

$A$ tuning fork gives $3$ beats with $50 \ cm$ length of sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork 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 .......... $Hz$.

The fundamental frequency '$n$' of a tuning fork is $288$ Hz. It will not resonate with which of the following frequencies (in $Hz$)?