This simulator adds two sine waves of slightly different frequency and displays both the resulting combined waveform and its slowly pulsing amplitude envelope — the phenomenon of beats. As the two frequencies drift in and out of phase with each other, the combined amplitude rises and falls at a rate equal to the difference between the two frequencies, exactly matching the throbbing "wah-wah-wah" you hear when two close musical pitches sound together.
• Two independently adjustable source frequencies close to each other, plus a shared amplitude control. • A live combined waveform showing the actual point-by-point sum of both tones. • A dashed envelope curve tracing the slowly-varying amplitude bound, which pulses at the beat frequency. • Live readouts for the beat frequency (the absolute difference between the two source frequencies) and the corresponding beat period.
When two waves of nearly equal frequency overlap, they drift in and out of phase with each other at a rate equal to their frequency difference. When they're momentarily in phase, they add constructively for a loud moment; a little later, they're out of phase and momentarily cancel for a quiet moment. This slow alternation between loud and quiet is the beat — its frequency is always simply |f₁ − f₂|, completely independent of how large f₁ and f₂ themselves are, which is exactly why piano tuners can hear beats slow to a stop as two strings converge on the same pitch.
Beats occur because two waves of slightly different frequency continuously drift in and out of phase with each other. When in phase they add constructively (loud); when out of phase they partially cancel (quiet) — this alternation repeats at the beat frequency.
Beat frequency equals the absolute difference between the two source frequencies: f_beat = |f₁ − f₂|. It does not depend on the actual values of f₁ or f₂, only on how far apart they are.
As two strings or pipes are tuned closer to the same pitch, the beat frequency between them slows down audibly. Tuners adjust until the beating disappears entirely, which confirms the two frequencies have converged to match.
It models two pure, equal-amplitude sine tones with no damping or harmonic content — it does not capture the complex overtone structure of real musical instruments, where beats can occur between individual harmonics rather than just the fundamental tones.