Two waves travelling in opposite directions produce a standing wave. The individual wave functions are given by ${\mathrm{y}}_1=4\sin (3\mathrm{x}-2\mathrm{t})\text{ and }{\mathrm{y}}_2=4\sin (3\mathrm{x}+2\mathrm{t})\mathrm{cm}$, where x and y are in cm$\left(\mathrm{Take} \sin 6.9 \mathrm{rad}=0.57875\right)$

$\begin{array}{l}\mathrm{y}={\mathrm{y}}_1+{\mathrm{y}}_2\\ \mathrm{y}=4[\sin (3\mathrm{x}-2\mathrm{t})+\sin (3\mathrm{x}+2\mathrm{t}\left)\right]\\ \mathrm{y}=4[2\sin (3\mathrm{x})\cos (2\mathrm{t}\left)\right]\\ \mathrm{y}=8\sin \left(3\mathrm{x}\right)\cos \left(2\mathrm{t}\right)\\ \mathrm{y}=\mathrm{Rcos}\left(2\mathrm{t}\right)\\ \mathrm{R}=\text{ Resultant Amplitude }=8\sin \left(3\mathrm{x}\right)\\ \mathrm{R}=8\sin \left[3\right(2.3\left)\right]\\ \mathrm{R}=8\sin (6.9)\\ \mathrm{R}=4.63\mathrm{cm}\end{array}$

Nodes are formed at points of zero intensity, i.e.,

$\begin{array}{l}{\mathrm{I}}_{\mathrm{R}}={\mathrm{R}}^2=0\\ {\sin }^2\left(3\mathrm{x}\right)=0\\ \sin \left(3\mathrm{x}\right)=0\\ 3\mathrm{x}=0,\mathrm{\pi },2\mathrm{\pi },3\mathrm{\pi },4\mathrm{\pi },\dots \\ \mathrm{x}=0,\frac{\mathrm{\pi }}{3},\frac{2\mathrm{\pi }}{3},\mathrm{\pi },\frac{4\mathrm{\pi }}{3},\dots \end{array}$

Antinodes are formed in between for the values of x.

$\mathrm{x}=\frac{\mathrm{\pi }}{6},\frac{3\mathrm{\pi }}{6},\frac{5\mathrm{\pi }}{6},\dots$