This phenomenon is best known in acoustics or music, though it can be found in any linear system: "According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes". Constructive and destructive interference can be seen.
The two waves are initially identical, then the frequency of the green wave is gradually increased by 25%. Mathematics and physics of beat tones The sum (blue) of two sine waves (red, green) is shown as one of the waves increases in frequency. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a combination tone is produced. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. With tuning instruments that can produce sustained tones, beats can be readily recognized. In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. Term in acoustics Diagram of beat frequency
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