What causes the formation of beats in sounds?

$A$ 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 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 harmonic waves moving in the same direction superimpose to form a wave $x = a \cos(1.5 t) \cos(50.5 t)$ where $t$ is in seconds. Find the period with which they beat (close to the nearest integer). (in $s$)

Two tuning forks $A$ and $B$ sounded together give $6$ beats per second. With an air resonance tube closed at one end,the two forks give resonance when the two air columns are $24 \, cm$ and $25 \, cm$ respectively. Calculate the frequencies of the forks.

$56$ tuning forks are arranged such that each fork produces $4$ beats per second with its previous one. If the frequency of the last fork is twice that of the first, the frequency of the $19^{\text{th}}$ fork is . . . . . . (in $\text{Hz}$)