The periodic waves of intensities I₁ and  I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is: 

The resultant intensity of two periodic waves at a point is given by

$\mathrm{I}={\mathrm{I}}_1+{\mathrm{I}}_2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}\cdot \cos \varphi$

Resultant intensity is maximum if

$\begin{array}{l}\cos \phi =-1\\ \text{ i.e. }{I}_{max}=I_1+I_2+2\sqrt{I_1{I}_2}\end{array}$

Resultant intensity is minimum if 

.$\begin{array}{l}\cos \phi =+1\\ \text{ i.e, }{\mathrm{I}}_{\text{tinin }}=\mathrm{I}+\mathrm{I},-2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}\end{array}$

Therefore, the sum of the maximum and rrumrnum intensities is  $I_{max}+I_{min}$

$\begin{array}{l}={\mathrm{I}}_1+{\mathrm{I}}_2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}+{\mathrm{I}}_1+{\mathrm{I}}_2-2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}\\ =2\left({\mathrm{I}}_1+{\mathrm{I}}_2\right)\end{array}$