Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t$. The number of beats produced per minute is

$A$ tuning fork vibrates with $2$ beats in $0.04$ seconds. The frequency of the fork is .... $Hz$.

An observer while going on a scooter hears the sound of two sirens of the same frequency from two opposite directions. If he travels along the direction of one of the sirens,then he:

Two tuning forks $A$ and $B$ are sounded together and produce $4$ beats per second. The frequency of tuning fork $A$ is $320 \,Hz$. When tuning fork $B$ is loaded with wax,the number of beats per second remains $4$. What is the frequency of tuning fork $B$ 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?

Two tuning forks of frequencies $320 \,Hz$ and $480 \,Hz$ are sounded together to produce sound waves. The velocity of sound in air is $320 \,ms^{-1}$. The difference between the wavelengths of these waves is nearly: (in $cm$)