Two waves $y = 0.25 \sin(316t)$ and $y = 0.25 \sin(310t)$ are travelling in the same direction. The number of beats produced per second will be:

An unknown frequency $x$ produces $8$ beats per second with a frequency of $250 \ Hz$ and $12$ beats per second with a $270 \ Hz$ source. Then $x$ is .... $Hz$.

$41$ tuning forks are arranged in increasing order of frequency such that each produces $5 \text{ beats/second}$ with the next tuning fork. If the frequency of the last tuning fork is double that of the frequency of the first fork,then the frequency of the first and last fork is:

$A$ tuning fork of frequency $n$ produces $x$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

$5\, \text{beats/second}$ are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95\, \text{m}$ or $1\, \text{m}$. The frequency of the fork will be ... $\text{Hz}$.

$A$ 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 $Hz$)