🥁 Beats Production
📖 The Physics
Play two notes of nearly equal frequency together and something curious happens: the sound gets rhythmically louder and softer. When the two waves are in step they add up and the sound is loud; a moment later they are opposite and cancel, so it is silent.
These regular loud–soft pulses are called beats, and the yellow dashed line traces their slow rise and fall (the envelope).
y = sin(2πf₁t) + sin(2πf₂t) = 2·cos(π·Δf·t)·sin(2π·f_avg·t)
Beat frequency = |f₁ − f₂|
Set f₁ = f₂ and the beats vanish (a steady tone). The further apart the frequencies, the more beats per second — musicians use this to tune instruments until the beats disappear.
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