Two nearly identical rhythms combine into a slow pulse.
The sum-to-product identity separates a fast oscillation from a slowly varying amplitude. The absolute value of the amplitude envelope repeats |f₁−f₂| times each second. This display models a sum of waves; it does not play audio.
The signed envelope changes sign. Beat maxima follow its absolute magnitude, so counting only positive envelope peaks gives the wrong rate.
The audible beat rate corresponds to the absolute amplitude envelope. Equal frequencies produce a single doubled-amplitude wave.