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Two 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

Asked in NEET 2008 · Interference of two waves

Answer: (2) 2(I₁+I₂)

Step-by-step solution

Idea: intensity goes as the square of the amplitude, so write both extremes in terms of √I₁ and √I₂ and add.

Iₘₐₓ=(√I₁+√I₂)²=I₁+I₂+2√I₁I₂.

Iₘᵢₙ=(√I₁-√I₂)²=I₁+I₂-2√I₁I₂.

Adding, the cross terms cancel.

Iₘₐₓ+Iₘᵢₙ=2(I₁+I₂).

Why the other options are wrong

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