Question

Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive 90° out of phase is ______.

`[cos  pi/2=0]`

Options

• 2 : 1

• `sqrt2:1`

• 1 : 2

• 4 : 1

Answer 1

Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive 90° out of phase is 2 : 1.

Explanation:

`I=4I_0  cos^2  phi/2`

where Φ = 0, I₁ = 4I₀

when Φ = 90°, `I_2=4Icos^2 45^circ=4I_0xx1/2=2I_0`

`thereforeI_1/I_2=(4I_0)/(2I_0)=2`