PPolySim OS

Beats & Superposition

Two tones nearly in tune add up to a wave that swells and fades — the beats a musician listens for when tuning an instrument.

Beats & SuperpositionLive

Controls

Two tones close in frequency add to a wave whose amplitude throbs at the difference frequency — the beats a musician hears when tuning.

Presets

▶ Run in Python

Data Inspector

f₁, f₂10, 11
Beat frequency1.0
Effectamplitude throb

Governing equation

Reading this result: At a 1.0 Hz beat the throb is too fast to count as a pulse; the ear stops hearing separate beats and instead hears roughness or dissonance around the 10.5 Hz average pitch.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →
★ Sign in to save this setup
Save your tuned setup, or drop this simulation into your own site, docs, or course page.

How it works

When two waves of slightly different frequency superpose, their sum is modulated by an envelope that oscillates at the difference of the two frequencies. This beating is used to tune instruments and to detect tiny frequency differences with great precision.

Ask the AI about this model

The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

Related live simulations

Frequently asked questions

Is this acoustic beats tool really free?
Yes. Beats & Superposition runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.