Waves & Optics · 02 / 06

Superposition & Interference

When waves overlap, their instantaneous displacements add. Interference is not a separate force—it is the pattern produced by ordinary superposition.

The learner question

How can two waves share the same place without blocking each other?

In a linear medium, each wave contributes independently. At every point, the actual displacement is simply the algebraic sum of those contributions.

Superposition principle
ytotal=y1+y2y_{total}=y_1+y_2

Phase determines whether the two contributions reinforce, partially cancel, or fully cancel at a given point.

Interference lab

Slide one wave through phase and watch the resultant change.

strong reinforcement
wave 1wave 2resultant
phase offset
resultant amplitude
2.00
relationship
strong reinforcement
Amplitude A₁1.00
Amplitude A₂1.00
Phase offset0.00 cycle
interference idea
Constructive interference

When equal-frequency waves arrive nearly in phase, crest aligns with crest and trough with trough, so the resultant amplitude grows.

interference idea
Destructive interference

When equal-amplitude waves differ by half a cycle, each crest aligns with a trough and the resultant can vanish locally.

interference idea
The waves continue afterward

Interference does not normally destroy the original waves. After overlapping, each component continues according to the medium's wave equation.

Phase matters

Equal frequency alone does not determine interference. Relative phase decides the alignment of peaks and troughs.

Interference can vary through space

When path lengths differ, the phase difference can change from point to point, creating alternating maxima and minima.

Intensity is not amplitude

For many waves, measured intensity scales with amplitude squared, so doubling amplitude can quadruple intensity.

Transfer check

Two equal-amplitude sine waves have the same frequency and differ in phase by exactly half a cycle. What is their resultant?

← Wave Motion
Next: Reflection & Refraction · planned