What Is Superposition of Waves?

Superposition of waves occurs when two or more waves overlap: the resultant displacement at any point equals the algebraic sum of the individual wave displacements at that point. This principle is part of IB Physics C.3 Wave phenomena for both SL and HL.

How Superposition Works

1. Each wave produces its own displacement from the equilibrium position.
2. While the waves overlap, their displacements are added, including their positive or negative signs.
3. After overlapping, the waves continue travelling with their original shape, speed and direction, provided the medium behaves linearly.

If two waves produce displacements $y_1$ and $y_2$, the resultant displacement is

$$y_{\text{resultant}}=y_1+y_2.$$

For example, if one pulse produces a displacement of $+3.0\text{ cm}$ and another produces $-1.0\text{ cm}$, the resultant displacement is

$$y_{\text{resultant}}=+3.0+(-1.0)=+2.0\text{ cm}.$$

Superposition produces different forms of interference:

For continuous coherent waves, constructive interference occurs when the path difference is $n\lambda$. Destructive interference occurs when the path difference is $\left(n+\frac{1}{2}\right)\lambda$, where $n$ is an integer.

A common misconception is that waves permanently destroy or merge with each other. They do not: destructive interference gives zero displacement only while the waves overlap. Energy is redistributed within an interference pattern rather than simply disappearing.

IB Exam Technique

For a pulse diagram, add the signed displacement at corresponding positions, not the amplitudes alone. In an Explain question, state the superposition principle and connect the phase or path difference to constructive or destructive interference. This principle also underpins double-source interference and standing waves.