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Add two sinusoidal waves and watch superposition happen: choose interference, a standing wave, or beats, set each wave’s amplitude, frequency and phase, and see the two components and their resultant drawn on one axis — with wavelength, speed (v = fλ), period, k and ω updating live. It makes the big ideas visible: waves add, equal waves out of phase cancel, opposite-travelling waves make nodes and antinodes, and close frequencies produce beats. One-dimensional sinusoidal model, matching the IGCSE 0625 and IB core.
Wave 1
Wave 2
| Wave | f (Hz) | λ = v/f (m) | T = 1/f (s) | k = 2π/λ | ω = 2πf |
|---|---|---|---|---|---|
| 1 | 2.0 | 5.00 | 0.500 | 1.257 | 12.57 |
| 2 | 2.0 | 5.00 | 0.500 | 1.257 | 12.57 |
Model: superposition of two 1D sinusoidal waves, y = A·sin(kx ∓ ωt + φ), with a shared medium speed (v = fλ). Interference, standing-wave and beats modes (CAIE 0625 §3.1 / IB C.3–C.4). 2D ripple-tank, double-slit, non-sinusoidal (Fourier) and dispersion are out of scope. Values are computed in full precision and rounded for display. Educational tool — a guide for understanding, not a substitute for exam practice.
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Last updated: July 2026
Superposition, v = fλ, interference, standing waves and beats.
The principle of superposition says that when two or more waves meet at the same point, the total displacement at that point is the sum of the displacements each wave would produce on its own. The simulator draws the two component waves and their sum (the resultant) on the same axis, so you can see the resultant rise where the waves reinforce and cancel where they oppose.
The wave equation is v = f·λ: wave speed equals frequency times wavelength. The period is T = 1/f (the time for one full oscillation), the angular frequency is ω = 2πf, and the wave number is k = 2π/λ. In the simulator the medium speed v is shared by both waves, so choosing a frequency fixes the wavelength through λ = v/f — exactly the relationship these formulas describe.
When two identical waves meet in phase (phase difference 0, 360°, …) they reinforce — constructive interference — and the resultant amplitude is at its largest, 2A for two waves of amplitude A. When they meet exactly out of phase (180°) they cancel — destructive interference — and the resultant is zero. For any phase difference Δφ between two equal waves, the resultant amplitude is 2A·|cos(Δφ/2)|; sweeping the phase slider walks you through the whole range.
A standing wave forms when two identical waves travel in opposite directions and superpose, giving y = 2A·sin(kx+φ)·cos(ωt) — a pattern that oscillates in place rather than travelling. Nodes are points that never move (zero displacement at all times); antinodes are the points of maximum swing, reaching amplitude 2A. Neighbouring nodes are half a wavelength apart (spacing = λ/2), which the standing-wave mode marks on the axis.
It covers the superposition of two 1D sinusoidal waves in three bounded cases — interference (same direction), standing waves (opposite directions) and beats (two slightly different frequencies, where the beat frequency equals |f₁ − f₂|). This matches the Cambridge IGCSE 0625 general wave properties and the IB C.3–C.4 core. Two-dimensional ripple-tank and double-slit patterns, non-sinusoidal (Fourier) waveforms and dispersion are deliberately out of scope — the same way this tool keeps the model to the examinable sinusoidal case.
Waves reward a feel for the relationships — v = fλ, what stays constant when a wave slows down, how phase difference controls interference. A GetYourTutors physics specialist who comes to your home in Dubai can connect the equations to what a wave actually does, work through past-paper interference and standing-wave questions, and clear up the phase and node/antinode ideas that most often cost marks.