Question

Two sinusoidal plane waves of the same frequency having intensities $I_0$ and $4I_0$ are travelling in the same direction. The resultant intensity at a point at which the waves meet with a phase difference of $\frac{\pi }{2}$ is

• A. $2I_0$
• B. $5I_0$
• C. $9I_0$
• D. $3I_0$

Answer 1

The correct option is B $5I_0$

We know that resultant intensity at a point is given by,
$I=I_1+I_2+2\sqrt{I_1{I}_2}\text{cos}\Delta \varphi$
$\Rightarrow I=I_0+4I_0+2\sqrt{I_0\times 4I_0}\text{cos}\frac{\pi }{2}$
$\Rightarrow I=5I_0$