Rankers Physics

Principle of Superposition, Interference and Beats: Practice Problem & Solution

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 (2008)
$(\sqrt{I_1} - \sqrt{I_2})^2$
$2(I_1 + I_2)$
$I_1 + I_2$
$(\sqrt{I_1} + \sqrt{I_2})^2$

Solution Explained:

To solve this problem, we apply the core principles of Principle of Superposition, Interference and Beats. Understanding the underlying formula is key to arriving at the correct answer below:

$I_{\text{max}} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{\text{min}} = (\sqrt{I_1} - \sqrt{I_2})^2$. Sum $= (I_1 + I_2 + 2\sqrt{I_1 I_2}) + (I_1 + I_2 - 2\sqrt{I_1 I_2}) = 2(I_1 + I_2)$.

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