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For Students · Beats

Beats 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.

Beats & SuperpositionLive

two close frequencies interfere

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

Frequency 1

Frequency 2

▶ Run in Python

Data Inspector

f₁, f₂10, 11

Beat frequency1.0

Effectamplitude throb

Governing equation

f_{beat} = ∣ f_{2} - f_{1} ∣ = ∣11 - 10∣ = 1.0 Hz

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.

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Frequently asked questions

Is this good for students?: Yes — this version of "Beats 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.