Question

Two coherent waves are represented by $y_1=a_1\cos \omega t$ and $y_2=a_2\sin \omega t$, superimposed on each other. The resultant intensity is proportional to

• A. $\left(a_1+a_2\right)$
• B. $\left(a_1-a_2\right)$
• C. $\left(a_1^2+a_2^2\right)$
• D. $\left(a_1^2-a_2^2\right)$

Answer 1

Answer: (C)

As, $y_1=a_1\cos \omega t=a_1\sin \left(\omega t+90^{\circ }\right)$
and $y_2=a_2\sin \omega t$
$\therefore$ Phase difference $=\varphi =90^{\circ }$
$R=\sqrt{a_1^2+a_2^2+2a_1{a}_2\cos \varphi }$
$=\sqrt{a_1^2+a_2^2}$
$\therefore$ Resultant intensity, $I\propto R^2$
$\Rightarrow I\propto \left(a_1^2+a_2^2\right)$