Beat Frequency
Interactive simulation — adjust parameters and watch the visualization update in real time.
How it works
When two tones are close in frequency, their superposition is a carrier at the average frequency modulated by a slowly varying amplitude. The loudness pulses at the beat frequency |f₁−f₂| — you hear ‘wah-wah’ beats. The canvas scrolls time; dashed lines show the envelope.
Key equations
s = 2 cos(πΔf t) sin(2πfₐᵥₑ t), fₐᵥₑ = (f₁+f₂)/2, Δf = f₁−f₂
Beat frequency (loudness maxima per second) ≈ |Δf| when amplitudes match.