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:

When an air column at $15 ^\circ C$ and a tuning fork are sounded together, $4$ beats per second are produced. The frequency of the fork is less than that of the air column. When the temperature falls to $10 ^\circ C$, the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0 ^\circ C = 332, m/s]$.

Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6$ beats per second when both wires vibrate simultaneously?

What is a beat? Obtain the equation for the number of beats produced in unit time.

$A$ tuning fork $A$ produces $5$ beats per second with a tuning fork of frequency $480 \ Hz$. When a little wax is stuck to a prong of fork $A$,the number of beats heard per second becomes $2$. What is the frequency of tuning fork $A$ before the wax is stuck to it (in $Hz$)?

On sounding tuning fork $A$ with another tuning fork $B$ of frequency $384 \ Hz$,$6$ beats are produced per second. After loading the prongs of $A$ with some wax and then sounding it again with $B$,$4$ beats are produced per second. What is the frequency of the tuning fork $A$ in $Hz$?