Superposition principle

Superposition occurs when two or more waves overlap, resulting in a combined wave. The superposition principle states that this combined wave's displacement is the vector sum of the individual waves' displacements.

Constructive Interference - Constructive interference occurs when the waves are in phase and a crest of one wave meets the crest of another wave.

Destructive Interference - Destructive interference occurs when the waves are out of phase and the crest of one wave meets the trough of another wave.

Phase difference

Phase difference is a measure of how much one wave is shifted or lagged relative to the other, measured in degrees or radians.

In phase -If both waves are at the same cycle stage and moving identically, they are said to be in phase with a phase difference of 0°.

Out of phase - When waves are completely out of phase, the crest of one wave meets the trough of another wave. This happens when they are half a cycle apart, corresponding to a phase difference of 180° or $\pi$ rad.

Role of path difference in interference

Path difference, the varied distances waves travel, influences whether interference is constructive or destructive.

Constructive interference - occurs when the path difference is an integer number (n) of wavelengths $\lambda$.

$ \text{path difference = n}\lambda $

Destructive interference - occurs where there is a path difference equal to an odd number of half wavelengths.

$ \text{path difference = }\frac{(2n+1)\lambda}{2}=\left(n+\frac{1}{2}\right)\lambda $