Question

Two interfering waves having intensities x and y meets a point with time difference 3T/2. What will be the resultant intensity at that point

• A. $(\sqrt{x} + \sqrt{y})$
• B. $(\sqrt{x} + \sqrt{y} + \sqrt{xy})$
• C. $x + y + 2\sqrt{xy}$
• D. $\frac{x + y}{2xy}$

Answer 1

Answer: (C)

$x + y + 2\sqrt{xy}$

Answer 2

Time difference T.D. $= \frac{T}{2\pi} \times \varphi$ ⇒ $\frac{3T}{2} = \frac{T}{2\pi} \times \varphi$ ⇒ $\varphi = 3\pi;$ This is the condition of constructive interference.

So resultant intensity

$I_{R} = (\sqrt{I_{1}} + \sqrt{I_{2}})^{2} = (\sqrt{x} + \sqrt{y})^{2} = x + y + 2\sqrt{xy}.$