Question

Suppose displacement produced at some point $P$ by a wave is $y_1=acos\omega t$ and by another wave is $y_2=acos\omega t$.Let $I_0$ represents intensity produced by each one of individual wave, then resultant intensity due to overlapping of both wave is

• A. $I_0$
• B. $2I_0$
• C. $\frac{I_0}{2}$
• D. $4I_0$

Answer 1

The correct option is D $4I_0$

$y_{res}$ at point $P=y_1+y_2=a\cos \omega t+a\cos \omega t=2\cos \omega t$

Now amplitude $=2a$

Since intensity $\propto$(amplitude)${}^2$

So, $\frac{I_{new}}{I_0}=\frac{4a^2}{a^2}⟹I_{new}=4I_0$