In case of superposition of waves (at x=0). $y_1=4\sin \left(1026\pi t\right)$ and $y_2=2\sin \left(1014\pi t\right)$ 

$\begin{array}{l}\mathrm{y}={\mathrm{y}}_1+{\mathrm{y}}_2\\ =2\sin \left(1026\mathrm{\pi t}\right)+4\cos \left(6\mathrm{\pi t}\right)\sin \left(1020\mathrm{\pi t}\right)\\ \mathrm{Frequency} \mathrm{of} \mathrm{resulting}\mathrm{wave}=\frac{\mathrm{\omega }}{2\mathrm{\pi }}=\frac{1020\mathrm{\pi }}{2\mathrm{\pi }}=510\mathrm{Hz}\\ \mathrm{Amplitude} \mathrm{of} \mathrm{resulting}\mathrm{wave}\mathrm{varies}\mathrm{at}\mathrm{frequency}=\frac{\mathrm{\omega }}{2\mathrm{\pi }}=\frac{6\mathrm{\pi }}{2\mathrm{\pi }}=3\mathrm{Hz}\\ {\mathrm{f}}_{\mathrm{beat}}=\frac{12\mathrm{\pi }}{2\mathrm{\pi }}=6\mathrm{Hz}\end{array}$

$\frac{l_{max}}{l_{min}}=\frac{{\left(a_1+a_2\right)}^2}{{\left(a_1-a_2\right)}^2}=\frac{(4+2{)}^2}{(4-2{)}^2}=\frac{36}{4}=\frac{9}{1}$