Question

Two waves of same amplitude and same intensity interfere at one point. Phase difference between them is $\theta$. Match the following two columns.

Answer 1

The two waves of same amplitude $A_o$ and same intensity $I_o$ interfere at one point.

Thus resultant amplitude $A_R=2A_{o}cos\frac{\theta }{2}$

(A) : $\theta ={60}^o$ $⟹\frac{\theta }{2}={30}^o$

$\therefore$ $A_R=2A_{o}cos{30}^o=2A_o\times \frac{\sqrt{3}}{2}=\sqrt{3}{A}_o$

(B) : $\theta ={120}^o$ $⟹\frac{\theta }{2}={60}^o$

$\therefore$ $A_R=2A_{o}cos{60}^o=2A_o\times \frac{1}{2}=A_o$

Resultant intensity $I_R=4I_{o}co{s}^2\frac{\theta }{2}$

(C) : $\theta ={90}^o$ $⟹\frac{\theta }{2}={45}^o$

$\therefore$ $I_R=4I_{o}co{s}^2{45}^o=4I_o\times (\frac{1}{\sqrt{2}}{)}^2=2I_o$

(D) : $\theta =0^o$ $⟹\frac{\theta }{2}=0^o$

$\therefore$ $I_R=4I_{o}co{s}^2{0}^o=4I_o\times 1=4I_o$