〰 Wave Physics Game

Wave Interference — Free Online Wave Superposition Physics Game

Wave Interference renders a live 2D interference field in real time — every pixel shows the superposition of your wave sources. Drag sources to reshape the pattern and hit constructive or destructive interference targets across 8 levels of increasing complexity.

The physics behind the game

Wave superposition

y_total = Σ Aᵢ·sin(kᵢrᵢ − ωt + φᵢ)

Every point in space receives contributions from all sources simultaneously. The amplitudes simply add — this is the principle of superposition, valid for all linear waves.

Constructive interference

Δr = nλ (n = 0, 1, 2…)

When two waves arrive with path lengths differing by a whole number of wavelengths, their crests and troughs align — amplitude doubles.

Destructive interference

Δr = (n + ½)λ

When path lengths differ by a half-wavelength, crests meet troughs — the waves cancel. This is the principle behind noise-cancelling headphones.

Standing waves

y = 2A·cos(kx)·sin(ωt)

Two waves of equal frequency travelling in opposite directions create a standing wave — nodes (zero amplitude) and antinodes (maximum amplitude) fixed in space.

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Wave Superposition, Interference, and Diffraction

The Superposition Principle

When waves overlap, total displacement = algebraic sum of individual displacements: y_total = y₁ + y₂ + … Constructive interference: waves in phase (path difference = nλ). Amplitudes add: A_total = A₁ + A₂. Intensity ∝ A² — four times the intensity from two equal-amplitude waves in phase. Destructive interference: out of phase (path difference = (n+½)λ). Amplitudes cancel: A_total = 0. Energy is not destroyed — redistributed from dark to bright regions (energy conservation).

Young's Double-Slit: y = λD/d

Two slits, separation d, wavelength λ, screen distance D. Bright fringe spacing: y = λD/d. Bright fringes (constructive): d sinθ = nλ. Dark fringes (destructive): d sinθ = (n+½)λ. Wider slit separation → narrower fringes. Longer wavelength → wider fringes. This experiment proved in 1801 that light is a wave (Young). When performed with single photons fired one at a time, interference still appears — proving wave-particle duality: each photon passes through both slits as a wave.

Diffraction and Huygens' Principle

Huygens (1678): every point on a wavefront is a source of secondary wavelets; the new wavefront is their envelope. This explains why waves bend around corners (diffraction) — especially when the aperture/obstacle size is comparable to λ. Single-slit diffraction: minimum intensity at sin θ = mλ/a (a = slit width). First minimum at θ₁ = λ/a. Diffraction limits the resolution of optical instruments: Rayleigh criterion θ_min = 1.22λ/D (D = lens diameter). Electron microscopes use λ_de Broglie ≈ 1 pm to image atoms.

WaveInterference