Superposition: Why Waves Pass Through Each Other

Lesson notes

Key points

• Because the wave equation is linear, any sum of two solutions is also a solution.
• So where two pulses overlap, the displacement is simply the algebraic sum of each pulse's displacement.
• Crests adding to crests give constructive interference, while a crest meeting an equal trough gives destructive interference.
• Energy is not destroyed during cancellation; it is redistributed, and each pulse emerges with its original shape.

Definitions

Superposition principle

Net displacement at a point equals the sum of the displacements of each individual wave there.

Takeaway: Overlapping waves simply add; linearity makes it possible.}

LinearitySuperpositionInterferenceEnergy redistributed