Waveform Shape & Interference Patterns

Wave Interference

Source separation 3.2

Wavelength 1.4

Phase offset 0°

Harmonics summed

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Peak amplitude

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Fringe spacing (fund.)

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How it works

Two point sources emit an identical periodic waveform outward as circular ripples across the surface. Every vertex simply adds the displacement contributed by each source arriving at that point — the principle of superposition. A sine wave is a single frequency, so the result is the smooth double-slit fringe pattern. Square and triangle waves are secretly sums of many sine harmonics (Fourier's theorem), and each harmonic interferes at its own, shorter wavelength — so the combined surface shows a sharper, less evenly spaced pattern even though nothing about the physics changed.

y(x,z,t) = Σ_sources Σ_harmonics Aₙ · sin(2π(dᵢ/λₙ − f·t) + φᵢ)
square:   λₙ = λ/n, Aₙ = 1/n, n = 1,3,5…
triangle: λₙ = λ/n, Aₙ = 1/n², n = 1,3,5…

Waveform — sine uses one frequency; square and triangle add odd harmonics (3f, 5f, 7f…) that each build their own, tighter interference pattern layered on top of the fundamental's.
Source separation — how far apart the two emitters sit; wider separation packs more bright/dark fringes into the same field of view.
Wavelength — the fundamental's wavelength; shorter wavelengths pack fringes tighter, same as increasing separation.
Phase offset — shifts source 2 relative to source 1; 180° flips every constructive point into a destructive one, harmonic by harmonic.

Real-world relevance: loudspeaker arrays, phased antennas and Young's double-slit experiment all rely on this same superposition rule — and none of them emit pure sine waves, so every harmonic's fringe pattern must be accounted for separately.

Crest (constructive) Trough (destructive) Source

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