$56$ 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 ..... $Hz$.

$A$ 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 $Hz$)?

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

The wavelength of one wave is $99 \ cm$ and that of another is $100 \ cm$. If the speed of sound is $396 \ m/s$,the number of beats heard per second is:

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 $Hz$)?

Two sound waves of wavelengths $\lambda_1$ and $\lambda_2$ $(\lambda_2 > \lambda_1)$ produce $n$ beats per second. The speed of sound is: