Beats occur when two sounds waves of similar frequencies interfere with each other. When the peaks of one wave align with the troughs of the other, they cancel each other out, creating a distinctive "dum" sound. This happens periodically as the waves go in and out of phase, producing the rhythm of beats. Beats can be visualized mathematically as a combination of two sinusoidal waves, with the amplitude defined by a boundary that creates the distinct pulses we hear. The frequency of these pulses is governed by both the mean angular frequency and the angular frequency difference between the original waves.