Understanding Wave Combination: 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.

Graph showing wave superposition with examples of constructive and destructive interference. Constructive interference occurs when the waves are in phase, and destructive interference occurs when the waves are out of phase.

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.

Superposition

This lesson covers: 

  1. Superposition principle in wave combination
  2. Types of wave interference: constructive and destructive
  3. Phase difference
  4. Impact of path difference on interference

Phase Difference

Diagram showing waves in phase, out of phase, and completely out of phase.

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 π 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 λ.


path difference = nλ


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


path difference = 2(2n+1)λ​=(n+21​)λ