If three sources of sound of frequencies $(n-1)$, $n$, and $(n+1)$ are vibrated together, the number of beats produced and heard per second respectively are

Two sound waves having displacements $x_1 = 2 \sin(1000 \pi t)$ and $x_2 = 3 \sin(1006 \pi t)$,when interfere,produce

$A$ tuning fork of known frequency $256\,Hz$ produces $5$ beats per second with the vibrating string of a guitar. The beat frequency decreases to $2$ beats per second when the tension in the guitar string is slightly increased. The frequency of the guitar string before increasing the tension was ..... $Hz$.

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

Two waves $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating along the same direction. The number of beats produced per second is:

$A$ tuning fork vibrates with $2$ beats in $0.04$ seconds. The frequency of the fork is .... $Hz$.