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 .... $Hz$.

$A$ sound wave travels with a velocity of $300 \, m \, s^{-1}$ through a gas. $9$ beats are produced in $3 \, s$ when two waves pass through it simultaneously. If one of the waves has a wavelength of $2 \, m$, the wavelength of the other wave is ..... $m$.

Draw graphs of beats produced by two harmonic waves of frequency $11 \ Hz$ and $9 \ Hz$.

$A$ tuning fork $A$ of frequency $200 \ Hz$ is sounded with fork $B,$ the number of beats per second is $5.$ By putting some wax on $A,$ the number of beats increases to $8.$ The frequency of fork $B$ is .... $Hz$

In a guitar,two strings $A$ and $B$ made of the same material are slightly out of tune and produce beats of frequency $6 \, Hz$. When the tension in $B$ is slightly decreased,the beat frequency increases to $7 \, Hz$. If the frequency of $A$ is $530 \, Hz$,the original frequency of $B$ will be $......... \, Hz$.

The frequency of a tuning fork is $n \ Hz$ and the velocity of sound in air is $V \ m/s$. When the tuning fork completes $x$ vibrations,the distance traveled by the wave is: