Music & Acoustics

Beat Frequency

cos 2πf₁t + cos 2πf₂t ; f_beat = |f₁−f₂|

Two tones one hertz apart add to a single carrier whose loudness swells and fades once per second — the beat rate you hear is exactly the difference |f₁−f₂| of the two frequencies.

Computed & rendered in pure C# on the frozen OnlyCSharp 1.8 library — animation baked to GIF with the library's own Gif encoder (no GPU, no ffmpeg, no external packages).