Question

Two sinusoidal plane waves of the same frequency having intensity $I_0$ and $4I_0$ are travelling in the same direction. The resultant intensity at a point at which waves meet with phase difference of zero radian is

• A. $I_0$
• B. $5I_0$
• C. $9I_0$
• D. $3I_0$

Answer 1

The correct option is C $9I_0$

Given,

$I_1=I_0;I_2=4I_0;\Delta \varphi =0^{\circ }$

Resultant intensity is given by,

$I_R=I_1+I_2+2\sqrt{I_1{I}_2}\cos \Delta \varphi [\because \cos 0^{\circ }=1]$

$I_R=[\sqrt{I_1}+\sqrt{I_2}{]}^2$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.

$I_R=[\sqrt{I_0}+\sqrt{4I_0}{]}^2=9I_0$