Wave Interference Simulator
Watch two waves combine in real time. Adjust frequency, amplitude, and phase of each wave to see constructive and destructive interference. Switch to the 2D ripple tank to see how two point sources create an interference pattern.
Wave Controls
Result
About Wave Interference
When two waves occupy the same space at the same time, their displacements add — this is the superposition principle. The result is a new wave whose shape depends on the frequencies, amplitudes, and relative phase of the components. This simulator lets you adjust each wave's parameters and watch the sum evolve in real time.
Constructive interference (Δφ = 0)
When two same-frequency waves are in phase, their peaks align and their troughs align. The sum amplitude is the literal sum of the individual amplitudes: A_sum = A₁ + A₂. Two identical waves combining constructively produce a wave twice as tall — but with the same energy density per cycle, so the sound (or light, or water wave) is 6 dB louder.
Destructive interference (Δφ = 180°)
When two same-frequency waves are opposite in phase, peaks of one align with troughs of the other and they cancel: A_sum = |A₁ − A₂|. Equal-amplitude waves cancel completely, leaving silence. This is exactly how noise-cancelling headphones work — they emit a sound that's 180° out of phase with the noise outside.
Beats (f₁ ≠ f₂)
If the two frequencies differ slightly, the relative phase drifts over time. The sum amplitude swells and fades at the beat frequency f_beat = |f₁ − f₂|. Musicians use this to tune instruments — when two strings are almost in tune, you hear the beat pulse slow down as they approach perfect pitch. At exactly in tune, beats vanish.
2D ripple tank
Two point sources emitting circular waves create an interference pattern in the plane. Along directions where the path difference to both sources is an integer number of wavelengths, the waves arrive in phase → bright fringes. Where the path difference is a half-integer multiple, they cancel → dark fringes. This is the foundation of Young's double-slit experiment, and the math is the same one used for radio antenna arrays and acoustic holography.
Frequently Asked Questions
What is "phase" intuitively?
Why does the sum amplitude depend on phase, not just amplitudes?
What's the difference between beats and interference?
Why do the 2D fringes shift when I change phase?
Is this a real wave simulation?
A·sin(k·d − ω·t + φ) for each source at each point and sum them, which is what the wave equation produces for linear superposition. Real ripple tanks add complications (boundary reflections, viscosity damping, finite source size, nonlinear effects at high amplitude) that this simulator doesn't model.What does "ω" mean and how does it relate to f?
ω = 2π·f. It comes from preferring to write sinusoidal functions as sin(ω·t) rather than sin(2π·f·t) — cleaner math, especially in calculus. Similarly k (wavenumber) = 2π/λ, so the wave equation sin(k·x − ω·t) describes a wave traveling at speed ω/k = f·λ.