Physics·TPC

Superposition Principle

Tsokos Ch. 11.3

Overview

When two or more waves are simultaneously present at the same point, the resultant displacement equals the algebraic sum of the individual displacements at that point. This is purely mathematical addition of amplitudes — applies to all types of waves. Constructive interference: waves in phase → amplitudes add. Destructive interference: waves out of phase → amplitudes cancel.

Superposition principle

When two or more waves overlap at the same point, the resultant displacement is the vector sum of the individual displacements: y_total = y₁ + y₂. This is the principle of superposition. After passing through each other, each wave continues unchanged (they don't permanently affect each other). This leads to interference patterns.

Constructive and destructive interference

Constructive interference: when two waves arrive in phase (path difference = 0, λ, 2λ, ...) — they add up, amplitude doubles. Destructive interference: when two waves arrive in antiphase (path difference = λ/2, 3λ/2, ...) — they cancel out, amplitude is zero. Conditions for coherent interference: same frequency, constant phase difference.

Worked Examples
Common Mistakes
  • Thinking waves 'destroy' each other permanently — they still pass through each other
  • Confusing path difference (in metres) with phase difference (in radians or degrees)