Wave Interference Calculator

Wave Interference When two coherent waves overlap, they interfere constructively (add) or destructively (cancel). Interference depends on the path difference (Δ) between the two sources to the observation point.

Constructive Interference Path difference Δ = m × λ (where m = 0, ±1, ±2, …) Amplitudes add: A_total = A₁ + A₂ Intensity is maximum: I_max = (A₁ + A₂)²

Destructive Interference Path difference Δ = (m + ½) × λ Amplitudes cancel: A_total = A₁ − A₂ I_min = (A₁ − A₂)² = 0 if equal amplitudes

Young’s Double-Slit Experiment Fringe spacing on a screen: Δy = λ × L / d Where: λ = wavelength (m) L = distance from slits to screen (m) d = slit separation (m) m-th bright fringe position: y_m = m × λ × L / d m-th dark fringe: y_m = (m + ½) × λ × L / d

Intensity Pattern (equal sources) I(θ) = I₀ × cos²(π × d × sin(θ) / λ) At angle θ from center axis.

Thin Film Interference Reflected light from top and bottom surfaces interferes. Constructive (including half-wave loss at denser medium): 2nt = (m + ½)λ → bright 2nt = mλ → dark (where n = film refractive index, t = film thickness)

Standing Waves Formed by two identical waves traveling in opposite directions. λ_n = 2L/n (n = 1, 2, 3, …) for string fixed at both ends f_n = nv/(2L), fundamental frequency f₁ = v/(2L)