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For Students · Additive Synthesis

Additive Synthesis for a standing wave

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a standing wave live below — adjust the inputs and watch it respond, right in your browser.

Additive SynthesisLive

building tone from sine waves

Controls

Presets

Harmonics

Any periodic waveform is a sum of sine harmonics — the basis of additive synthesis. A sawtooth needs every harmonic falling as 1/k; a square only odd harmonics; a triangle odd harmonics falling as 1/k². Add more harmonics to sharpen the shape, and watch the Gibbs overshoot ripple at the edges.

▶ Run in Python

Data Inspector

Waveformsawtooth

Harmonics8

Contentall

Governing equation

x (t) = k = 1 \sum 8 a_{k} sin (2 π k f t), a_{k} = \frac{1}{k}

Reading this result: The sawtooth needs every harmonic falling as 1/k; 8 of them sharpen the ramp but leave a Gibbs ripple at the jump.

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Frequently asked questions

Is this good for students?: Yes — this version of "Additive Synthesis for a standing wave" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.