What causes bright and dark regions?

Where crests from both sources meet in phase, amplitude adds (constructive interference); where they arrive out of phase, cancellation reduces amplitude (destructive interference).

Wave Interference

Two coherent sources in 2D produce an interference pattern of constructive and destructive regions. Adjust separation and wavelength to see how fringe spacing changes.

Who it's for: Physical optics and waves; Young’s experiment and path-difference reasoning.

Key terms

interference
path difference
constructive
destructive
coherence

Live graphs

Sources (bottom of tank)

L = side length of the square tank (all distances in units of L).

f and λ

Mathematical model: v = fλ is not enforced — k = 2π/λ and ω = 2πf are chosen independently (useful for visualization, confusing if you expect a single medium).

Separation d0.42 L

Wavelength λ0.18 L

Drive frequency f1.2 Hz

Phase of S₂ vs S₁ (φ₂−φ₁)0 °

Source strength1

Display gain1.15

Cylindrical 1/√r decayShow constructive / destructive guides

Superposition η = η₁ + η₂ with ηᵢ ∝ sin(kr − ωt + φᵢ) (optional geometric decay). Guides mark kΔr + Δφ ≈ 0 (bright) or π (dark) for equal amplitudes. Drag S₁ and S₂ on the tank.

Shortcuts

Space or Enter — pause / resume
R — reset time

Measured values

k = 2π/λ34.9071/L

ω = 2πf7.540rad/s

v = fλ0.2160L/s

|S₂−S₁|0.420 L

λ/d0.429

Far-field fringe spacing on a screen scales like (λ/d)·R (small-angle Young).

How it works

Two coherent point sources in a square ripple tank (top view). The field is the sum of two outgoing circular waves; interference creates quasi-hyperbolic nodal lines and curved maxima. Toggle decay to mimic cylindrical spreading.

Key equations

η = A₁ sin(kr₁ − ωt + φ₁) + A₂ sin(kr₂ − ωt + φ₂)

Path difference Δr = r₂ − r₁: with φ₁ = 0, bright zones when kΔr + φ₂ ≈ 2πn, dark when kΔr + φ₂ ≈ (2n+1)π (equal |A|). Young: fringe spacing ∝ λ/d.

Frequently asked questions

What causes bright and dark regions?: Where crests from both sources meet in phase, amplitude adds (constructive interference); where they arrive out of phase, cancellation reduces amplitude (destructive interference).