Simulate constructive and destructive interference of two waves. Adjust amplitude, frequency, and phase to see superposition.
Pick an amplitude, frequency, and phase for each of two waves, and the simulator draws their sum: the superposition. With equal frequencies the result is a single clean wave whose size follows a simple rule; the crests align for constructive interference and oppose for destructive. The surprise most users hit: two waves cancel completely only when their amplitudes are equal and their phase difference is exactly half a cycle. Unequal amplitudes never vanish, and different frequencies give no stable result at all - the sum swells and fades at the beat frequency instead.
A concrete input and expected output from the current implementation.
Input
Wave 1: amplitude 4, frequency 1 Hz, phase 0 degrees. Wave 2: amplitude 3, frequency 1 Hz, phase 90 degrees.
Expected output
A single 1 Hz sine wave with amplitude 5, leading wave 1 by about 37 degrees. Its peak reaches +5 and its trough -5. Neither 7 (the sum) nor 1 (the difference) appears.
At a 90 degree phase difference the waves neither reinforce nor cancel; the two amplitudes combine at right angles, so the resultant is the hypotenuse of the 3-4-5 triangle. Equal frequencies keep the sum a pure sine at the same frequency.
The tool samples both waves at the same instants and adds the two displacements. When the frequencies match, this sum is itself a perfect sine with amplitude sqrt(A1^2 + A2^2 + 2 A1 A2 cos d), where d is the phase difference; that single formula covers every case from full reinforcement (d = 0, amplitudes add) to full cancellation (d = 180 degrees, amplitudes subtract).
With different frequencies there is no fixed resultant shape. The sum oscillates inside an envelope that swells and dies out at the beat frequency, the absolute difference |f1 - f2|; for example, 10 Hz and 12 Hz beat at 2 Hz. Equal amplitudes give the deepest beats, dropping to silence at the nulls, which is why this is the classic setup for tuning instruments.
Verify both waves share one frequency and that the phase difference is exactly 180 degrees, not 179: the leftover amplitude is 2A sin(e/2) for an error of e, tiny at 1 degree but clearly nonzero at 10. Then check the phase box's units. If it reads radians, entering 180 means 180 radians, about 28 full cycles, and the pattern will not match anything you intended.
Only in a rough, first-step sense. The tool combines two waves at a single point; real speakers create waves spreading through space, so the result depends on distance, room reflections, and how the two paths differ. You can use it to confirm the amplitude logic, but the loud and quiet zones in a room are a spatial problem this simulator does not solve.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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