$A$ sound wave travels with a velocity of $300 \, m \, s^{-1}$ through a gas. $9$ beats are produced in $3 \, s$ when two waves pass through it simultaneously. If one of the waves has a wavelength of $2 \, m$, the wavelength of the other wave is ..... $m$.

$A$ tuning fork of frequency $100 \, Hz$ when sounded together with another tuning fork of unknown frequency produces $2$ beats per second. On loading the tuning fork whose frequency is not known and sounding it together with the tuning fork of frequency $100 \, Hz$,it produces one beat. The frequency of the other tuning fork is: (in $, Hz$)

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?

$A$ light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 \, cm$,the frequency of the tuning fork is .... $Hz$

Two stretched strings $A$ and $B$ when vibrated together produce $4$ beats per second. If the tension applied to the string $A$ is increased,the number of beats produced per second increases to $7$. If the frequency of string $B$ is $480 \ Hz$ initially,what is the frequency of string $A$ (in $Hz$)?

The maximum number of beats per second that a human ear can distinguish is