Phase Difference

Phase difference Δφ: how much one oscillation leads or lags another (in radians or degrees).

Two waves in PHASE (Δφ = 0, 2π, 4π…): crests align, displacements add (constructive).

Two waves OUT OF PHASE by π (180°): crest of one aligns with trough of other, cancel.

Phase difference from path difference: Δφ = (2π/λ)·Δx.

Constructive interference: Δφ = 2nπ (path difference = nλ).

Destructive: Δφ = (2n+1)π (path difference = (n+½)λ).

On phasor diagram: two oscillations are vectors with angle Δφ between them.

Phase difference can be due to: PATH difference, initial PHASE offset, REFRACTION through different medium, REFLECTION at boundary (which can add π).