When a tuning fork is vibrating,the vibrations of the two prongs

Beats are produced by two waves $y_1 = a \sin(1000 \pi t)$ and $y_2 = a \sin(998 \pi t)$. The number of beats heard per second is

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

$A$ tuning fork and an air column whose temperature is $51^{\circ} C$ produce $4$ beats in one second,when sounded together. When the temperature of the air column decreases,the number of beats per second decreases. When the temperature is $16^{\circ} C$,only one beat per second is produced. The frequency of the tuning fork is ........... $Hz$.

Two vibrating tuning forks produce progressive waves given by $Y_1 = 4\sin(500\pi t)$ and $Y_2 = 2\sin(506\pi t)$. The number of beats produced per minute is:

Two waves $y_1 = 0.35 \sin(316 t)$ and $y_2 = 0.35 \sin(310 t)$ are propagating along the same direction. The number of beats produced per second is: