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# The periodic waves of intensities I₁ and I₂ pass through a region at the same time

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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:

(a) I₁ + I₂
(b) (√I₁ + √I₂)²
(c) (√I₁ – √I₂)²
(d) 2 (I₁ + I₂)

2 (I₁ + I₂)

### Explanation:

The resultant intensity of two periodic waves at a point is given by
I = I₁ + I₂ + 2 √I₁I₂ . cos ?.
Resultant intensity is max. if cos ? = -1
i.e Iₘₐₓ = I₁ + I₂ + 2 √I₁I₂
Resultant intensity is min. if cos ? = +1
i.e, Iₘᵢₙ = I₁ + I₂ – 2 √I₁I₂
Therefore, the sum of the max. and min. intensities is Iₘₐₓ + Iₘᵢₙ
= I₁ + I₂ + 2 √I₁I₂ + I₁ + I₂ – 2 √I₁I₂
= 2 (I₁ + I₂)

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