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

$A$ prong of a vibrating tuning fork is in contact with the water surface. It produces concentric circular waves on the surface of the water. The distance between five consecutive crests is $0.8 \ m$ and the velocity of the wave on the water surface is $56 \ m/s$. The frequency of the tuning fork is: (in $Hz$)

$A$ tuning fork of known frequency $256\,Hz$ produces $5$ 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

Four tuning forks of frequencies $200 \, Hz, 201 \, Hz, 204 \, Hz$ and $206 \, Hz$ are sounded together. The beat frequency will be

$A$ pair of tuning forks produces $2$ beats in a time interval of $0.4 \ s$. The beat frequency is .... $Hz$.

The displacement at a point due to two waves are $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$. The result due to their superposition will be