Beats are produced by waves $y_1 = a \sin(2000 \pi t)$ and $y_2 = a \sin(2008 \pi t)$. The number of beats heard per second is

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

Two tuning forks when sounded together produce $4$ beats/sec. The frequency of one fork is $256 \, Hz$. The number of beats heard increases when the fork of frequency $256 \, Hz$ is loaded with wax. The frequency of the other fork is (in $, Hz$)

$A$ 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 .... $Hz$

$A$ 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 .... $Hz$

Two tuning forks of frequencies $320 \,Hz$ and $480 \,Hz$ are sounded together to produce sound waves. The velocity of sound in air is $320 \,ms^{-1}$. The difference between the wavelengths of these waves is nearly: (in $cm$)