Beat (acoustics) Totally Explained

Everything about Beat Acoustics totally explained

In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies.
When tuning instruments that can produce sustained tones, beats can readily be recognized. Tuning two tones to a unison will present a strange effect: when the two tones are close in pitch but not yet perfectly centered, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. When the two tones gradually approach fusion, the beating slows down and disappears, giving way to full-bodied unison resonance.

Mathematics and physics of beat tones

This phenomenon manifests acoustically. If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant as when a pure note is played, but change over time: when the two waves are nearly 180 degrees out of phase the maxima of each cancel the minima of the other, whereas when they're nearly in phase their maxima sum up, raising the perceived volume.
It can be proven (see List of trigonometric identities) that the successive values of maxima and minima form a wave whose frequency equals the difference between the two starting waves. Let's demonstrate the simplest case, between two sine waves of unit amplitude:
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equals one, the two waves are in phase and they interfere constructively. When it's zero, they're out of phase and interfere destructively. Beats occur also in more complex sounds, or in sounds of different volumes, though calculating them mathematically isn't so easy.
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (for example second overtone) of the bass note beats with the second harmonic (first overtone) of the other note.

Difference tones

Consider the two waves starting in unison, f = 0. As the difference between f₁ and f₂ increases, the speed increases. Beyond a certain proximity (usu. about 15 Hz), beating becomes undetectable and a roughness is heard instead, after which the two pitches are perceived as separate. If the beating frequency rises to the point that the envelope becomes audible (usually, much more than 20 Hz), it's called a difference tone. The violinist Giuseppe Tartini was the first to describe it, dubbing it il Terzo Suono (Italian for "the third sound"). Playing pure harmonies (for example, a frequency pair of a simple proportional relation, like 4/5 or 5/6, as in just intonation major and minor third respectively) on the two upper strings, such as the C above middle C against an open E-string, will produce a clearly audible C two octaves lower.
An interesting listening experiment is to start from a perfect unison and then very slowly and regularly increase the pitch of one tone. When one tone starts to split out from the former twin-note, a slow rumbling can be heard, gradually increasing into an audible tone.

Uses

Musicians commonly use interference beats to objectively check tuning at the unison, perfect fifth, or other simple harmonic intervals. Piano and organ tuners even use a method involving counting beats, aiming at a particular number for a specific interval.
The composer Alvin Lucier has written many pieces which feature interference beats as their main focus.

Binaural beats

Binaural beats are heard when the right ear listens to a slightly different tone than the left ear. Here, the tones don't interfere physically, but are summed by the brain in the olivary nucleus. This effect is related to the brain's ability to locate sounds in three dimensions. In addition, there are indications that binaural beats may have a psychological or neurological effect upon the listener.

Sample

Further Information

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