Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same…

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction, the sum of the maximum and minimum intensities is
  1. $(\sqrt{I_1} - \sqrt{I_2})^2$
  2. $2(I_1 + I_2)$
  3. $I_1 + I_2$
  4. $(\sqrt{I_1} + \sqrt{I_2})^2$

Solution

$I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1I_2}$ and $I_{\text{min}} = I_1 + I_2 - 2\sqrt{I_1I_2}$ $\therefore \quad \text{Sum of maximum and minimum intensities} = 2(I_1 + I_2)$

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