Equations of a stationary and a travelling waves are as follows ${\mathrm{y}}_1 = \mathrm{a} \sin \mathrm{kx} \cos \mathrm{\omega t} \mathrm{and} {\mathrm{y}}_2 = \mathrm{a} \sin \left(\mathrm{\omega t} - \mathrm{Kx}\right)$ The phase difference between two points ${\mathrm{x}}_1 = \frac{\mathrm{\pi }}{3\mathrm{k}} \mathrm{and} {\mathrm{x}}_2 = \frac{3\mathrm{\pi }}{3\mathrm{k}}$ are ${\mathrm{\varphi }}_1 \mathrm{and} {\mathrm{\varphi }}_2$ respectively for the two waves. The ratio $\frac{{\mathrm{\varphi }}_1}{{\mathrm{\varphi }}_2}$ is

$$\begin{gathered} \mathrm{At} {\mathrm{x}}_1 = \frac{\mathrm{\pi }}{3\mathrm{k}} \mathrm{and} {\mathrm{x}}_2 = \frac{3\mathrm{\pi }}{2\mathrm{k}} \\ \sin {\mathrm{Kx}}_1 \mathrm{or} \sin {\mathrm{Kx}}_2 \mathrm{is} \mathrm{not} \mathrm{zero}. \\ \mathrm{Therefore}, \mathrm{neither} \mathrm{of} {\mathrm{x}}_1 \mathrm{or} {\mathrm{x}}_2 \mathrm{is} \mathrm{a} \mathrm{node} \mathrm{\Delta x} = {\mathrm{x}}_2 - {\mathrm{x}}_1 = \left(\frac{3}{2} - \frac{1}{3}\right)\frac{\mathrm{\pi }}{\mathrm{k}} = \frac{7\mathrm{\pi }}{6\mathrm{k}} \\ Sin\mathrm{ce} \frac{2\mathrm{\pi }}{\mathrm{k}} > \mathrm{\Delta x} > \frac{\mathrm{\pi }}{\mathrm{k}} \\ \mathrm{\lambda } > \mathrm{\Delta x} > \frac{\mathrm{\lambda }}{2} \left(\mathrm{k} = \frac{2\mathrm{\pi }}{\mathrm{\lambda }}\right) \\ \mathrm{Therefore}, {\mathrm{\varphi }}_1 = \mathrm{\pi } \\ \mathrm{and} {\mathrm{\varphi }}_2 = \mathrm{k} \mathrm{\Delta x} = \frac{7\mathrm{\pi }}{6} \\ \therefore \frac{{\mathrm{\varphi }}_1}{{\mathrm{\varphi }}_2} = \frac{6}{7} \end{gathered}$$

Note : In case of stationary wave phase difference between any two points is either zero of $\mathrm{\pi }$ .