Interference

Interference: superposition of two or more waves resulting in a new pattern of amplitudes.

CONSTRUCTIVE (in phase, Δφ = 2nπ): amplitudes ADD ⇒ A_total = A₁ + A₂.

DESTRUCTIVE (out of phase by π, Δφ = (2n+1)π): amplitudes SUBTRACT ⇒ A_total = |A₁ − A₂|.

Generally: A_total = √(A₁² + A₂² + 2A₁A₂·cos Δφ).

Intensity: I ∝ A² ⇒ I_max = (A₁ + A₂)², I_min = (A₁ − A₂)² for coherent sources.

COHERENT sources required: constant phase relation and same frequency.

Examples: Young's double slit (light), two loudspeakers (sound), two-source interference patterns.

Path difference Δx → phase difference Δφ = 2π·Δx/λ. Bright fringe: Δx = nλ. Dark fringe: Δx = (n+½)λ.