Two sources of sound are emitting progressive waves $y_1 = 4 \sin 708 \pi t$ and $y_2 = 3 \sin 700 \pi t$. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and wanning are respectively

Two perfectly identical wires are in unison. When the tension in one wire is increased by $1\%$,then on sounding them together $3$ beats are heard in $2 \,s$. The initial frequency of each wire is .... $\text{s}^{-1}$.

$56$ tuning forks are arranged in increasing order of frequencies in a series such that each fork gives $4 \text{ beats per second}$ with the previous one. The frequency of the last fork is the octave of the first. The frequency of the first fork is ..... $Hz$.

Draw graphs of beats produced by two harmonic waves of frequency $11 \ Hz$ and $9 \ Hz$.

In a guitar,two strings $A$ and $B$ made of the same material are slightly out of tune and produce beats of frequency $6 \, Hz$. When the tension in $B$ is slightly decreased,the beat frequency increases to $7 \, Hz$. If the frequency of $A$ is $530 \, Hz$,the original frequency of $B$ will be $......... \, Hz$.

Two tuning forks $A$ and $B$ are sounded together giving rise to $8$ beats in $2$ s. When fork $A$ is loaded with wax, the beat frequency is reduced to $4$ beats in $2$ s. If the original frequency of tuning fork $B$ is $380$ Hz, then the original frequency of tuning fork $A$ is . . . . . . Hz.