When a tuning fork is vibrating,the vibrations of the two prongs

$P$ and $Q$ are two wires whose fundamental frequencies are $256 \ Hz$ and $382 \ Hz$ respectively. How many beats per second will be heard if the third harmonic of $P$ and the second harmonic of $Q$ are sounded together?

$A$ set of $24$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \, Hz$ beats per second with the preceding one and the frequency of the last tuning fork is two times that of the first fork,find the frequency of the $5^{th}$ tuning fork in $Hz$.

$A$ tuning fork of frequency $n$ produces $x$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

Tuning fork $F_1$ has a frequency of $256 Hz$ and it is observed to produce $6$ beats/second with another tuning fork $F_2$. When $F_2$ is loaded with wax,it still produces $6$ beats/second with $F_1$. The frequency of $F_2$ before loading was ..... $Hz$.

Two vibrating tuning forks produce progressive 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: