Question

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(a) 2 (I₁ + I₂)(b) I₁ + I₂(c) $(\sqrt{I_{1}}+\sqrt{I_{2}})^{2}$(d) $(\sqrt{I_{1}}-\sqrt{I_{2}})^{2}$

Answer 1

Answer is a - 2 (I₁ + I₂)

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

I = I₁ + I₂ + 2 √I₁I₂ . cos ?.

Where? is the phase difference between the waves.

Thus, 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)

Answer 2

Answer:

2(I1+I2)

Explanation:

I=√(I1)+√(I2)+2√(I1)√(I2)cos∆]

For maximum ∆=0° cos ∆=1

For minimum∆=180° cos ∆= -1

Hope it helps you!!!