Question

Intensities of two interfering waves are I₀ and 9I₀. The resultant intensity at a point at which waves meet with a phase difference of `pi/3` radian is ______.

Options

• 10I₀

• 8I₀

• 13I₀

• 16I₀

Answer 1

Intensities of two interfering waves are I₀ and 9I₀. The resultant intensity at a point at which waves meet with a phase difference of `pi/3` radian is 13I₀.

Explanation:

Let I₁ = I₀ and I₂= 9I₀

Resultant Intensity, 

I = I₁ + I₂ + 2 `sqrt("I"_1"I"_2)` cos `phi`

= I₀ + 9I₀ + 2 `sqrt("I"_0 9"I"_0)`  cos `pi/3`

= I₀ + 9I₀ + 2 `xx` 3I₀ `xx 1/2`

= I₀ + 9I₀ + 3I₀ = 13 I₀