beateffekt

Beateffekt, also known as beating, is a phenomenon in acoustics and signal processing that occurs when two waves with similar but not identical frequencies propagate together. The interference of the two waves causes the resulting sound to fluctuate in amplitude at a rate equal to the absolute difference of the frequencies, producing audible pulsations or “beats.”

Mathematically, two sinusoidal signals with frequencies f1 and f2 and equal amplitudes combine to yield a waveform whose envelope oscillates at the beat frequency fb = |f1 − f2|. A common form is s(t) = 2A cos(π(f1 − f2)t) cos(2πfavg t), where favg = (f1 + f2)/2. The carrier at favg is modulated by the slowly varying envelope, causing the perceived loudness to rise and fall at the beat frequency. The effect is most noticeable when the frequencies are close together, typically within a few tens of hertz.

Beateffekt has practical applications, notably in musical tuning, where players listen for beat rates to adjust pitch until the beats disappear or are minimized. It also appears in radio engineering and signal processing during mixing or heterodyning, where two signals produce a new frequency equal to their difference. The perceptual outcome can range from a single note with fluctuating volume to two distinct pitches when the frequency difference is large.

In German acoustics, the phenomenon is related to Schwebung, the traditional term for beats. Related concepts include interference, amplitude modulation, and spectral analysis.