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

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27°\mathrm{C}$, two successive resonances are produced at $20$ $ \mathrm{cm}$ and $73$ $\mathrm{cm}$ of column length. If the frequency of the tuning fork is $320$ $ \mathrm{Hz}$, the velocity of sound in air at $27°\mathrm{C}$ is,

Three sound waves of equal amplitudes have frequencies $(n-1)$, $n$, $(n+1)$. They superimpose to give beats. The number of beats produced per second will be