Question

For constructive interference the phase difference between two waves must be _________.

• A. $0,\pi ,2\pi ,3\pi ,......$
• B. $\pi ,3\pi ,5\pi ,7\pi ,....$
• C. $0,2\pi ,4\pi ,6\pi ,....$
• D. $0,3\pi ,6\pi ,9\pi ,....$

Answer 1

The correct option is C $0,2\pi ,4\pi ,6\pi ,....$

Constructive interference between two waves occurs when there path difference is equal to the integral multiple of $\lambda$.

For constructive interference, path difference $\Delta x=n\lambda$

Phase difference $\delta =\frac{2\pi }{\lambda }\Delta x$

$⟹$ $\delta =\frac{2\pi }{\lambda }\times n\lambda =2n\pi$

Hence for constructive interference, phase difference must be $0,2\pi ,4\pi ,6\pi ,........$