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| {{Refimprove|date=May 2013}}
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| [[Image:Beating Frequency.svg|thumb|214px|Diagram of beat frequency]]
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| In [[acoustics]], a '''beat''' is an [[Interference (wave propagation)|interference]] between two [[sound]]s of slightly different [[frequency|frequencies]], perceived as periodic variations in volume whose rate is the [[Difference (mathematics)|difference]] between the two frequencies.
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| With [[Musical tuning|tuning]] instruments that can produce sustained tones, beats can readily be recognized. 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. The volume varies like in a [[tremolo]] as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be inperceptible.
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| ==Mathematics and physics of beat tones==
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| [[File:WaveInterference.gif|thumb|The sum (blue) of two sine waves (red, green) is shown as one of the waves increases in frequency. The two waves are initially identical, then the frequency of the green wave is gradually increased by 25%. Constructive and destructive interference can be seen.]]
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| This phenomenon manifests acoustically. If a graph is drawn to show the [[Function (mathematics)|function]] corresponding to the total sound of two [[strings (music)|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 are nearly in phase their maxima sum up, raising the perceived volume.
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| 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 frequencies of the two starting waves. Let's demonstrate the simplest case, between two [[sine wave]]s of unit [[amplitude]]:
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| :<math>{ \cos(2\pi f_1t)+\cos(2\pi f_2t) } = { 2\cos\left(2\pi\frac{f_1+f_2}{2}t\right)\cos\left(2\pi\frac{f_1-f_2}{2}t\right) }</math><ref>[http://www.animations.physics.unsw.edu.au/jw/beats.htm Interference beats and Tartini tones]</ref>
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| If the two starting frequencies are quite close (for example, a difference of the order of few [[hertz]]), the frequency of the cosine of the right side of the expression above, that is (''f''<sub>1</sub>−''f''<sub>2</sub>)/2, is often too slow to be perceived as a [[Pitch (music)|pitch]]. Instead, it is perceived as a periodic variation of the first in the expression above (it can be said that the lower frequency cosine term, i.e. the second one, is an ''envelope'' for the faster wave, i.e. the first cosine term), whose frequency is (''f''<sub>1</sub> + ''f''<sub>2</sub>)/2, that is, the [[average]] of the two frequencies. However, because the human ear is not sensitive to the phase, only the amplitude or intensity of the sound, only the absolute value of the envelope is heard. Therefore, subjectively, the frequency of the envelope seems to have twice the frequency of the cosine, which means the audible beat frequency is:
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| :<math>f_{beat}=f_1-f_2\,</math>
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| This can be seen on the diagram on the right.
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| [[Image:Beat.png|thumbnail|[[File:Beat - superposition of 104hz and 110hz sine waves.ogg]]
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| A 110 Hz A sine wave (magenta; first 2 seconds), a 104 Hz G# sine wave (cyan; following 2 seconds), their sum (blue; final 2 seconds) and the corresponding envelope (red)]]
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| A physical interpretation is that when <math>\cos\left(2\pi\frac{f_1-f_2}{2}t\right)</math> equals one, the two waves are in phase and they [[Interference (wave propagation)|interfere]] constructively. When it is zero, they are out of phase and interfere destructively. Beats occur also in more complex sounds, or in sounds of different volumes, though calculating them mathematically is not so easy.
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| Beating can also be heard between notes that are near to, but not exactly, a [[harmony|harmonic]] [[interval (music)|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 (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned [[equal temperament]] intervals, because of the differences between them and the corresponding [[just intonation]] intervals: see [[Harmonic series (music)#Harmonics and tuning]].
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| ==Uses==
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| Musicians commonly use interference beats to objectively check [[Musical tuning|tuning]] at the [[unison]], [[perfect fifth]], or other simple harmonic intervals. Piano and [[Organ (music)|organ]] tuners even use a method involving counting beats, aiming at a particular number for a specific interval.
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| The [[composer]] [[Alvin Lucier]] has written many pieces that feature interference beats as their main focus. Italian composer [[Giacinto Scelsi]], whose mature style is grounded on microtonal oscillations of unisons, extensively explored the textural effects of interference beats, particularly in his late works such as the violin solos ''Xnoybis'' (1964) and ''L'âme ailée / L'âme ouverte'' (1973), which feature them prominently (note that Scelsi treated and notated each string of the instrument as a separate part, so that his violin solos are effectively quartets of one-strings, where different strings of the violin may be simultaneously playing the same note with microtonal shifts, so that the interference patterns are generated). Composer [[Phill Niblock]]'s music is entirely based on beating caused by microtonal differences. Also [[David First]].
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| == Binaural beats ==
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| {{Main|Binaural beat}}
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| Binaural beats are heard when the right ear listens to a slightly different tone than the left ear. Here, the tones do not 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.
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| ==Sample==
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| {{Listen|filename=beat.ogg|title=Beating waveforms (high frequency)|description=220 Hz A3 (left channel) and 207.65 Hz G#3 (right channel) beating at 12.35 Hz|pos=left|format=[[Ogg]]}}
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| {{Listen|filename=Beatfrequency.ogg|title=Beating waveforms (low frequency)|description=220 Hz A3 and 222 Hz tone beating at 2.0 Hz|pos=left|format=[[Ogg]]}}
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| {{clear}}
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| == See also ==
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| * [[Envelope (waves)]]
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| * [[Voix céleste]]
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| * [[Gamelan#Tuning|Gamelan tuning]]
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| * [[Heterodyne]]
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| * [[Interference (wave propagation)|Interference]]
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| * [[Consonance and dissonance]]
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| * [[Moiré pattern]], a form of spatial interference that generates new frequencies.
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| ==References==
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| {{Reflist}}
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| == External links ==
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| * [http://www-math.mit.edu/daimp/Beats.html Java applet], MIT
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| * [http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html Acoustics and Vibration Animations], D.A. Russell, Kettering University
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| *[http://phy.hk/wiki/englishhtm/Beats.htm A Java applet showing the formation of beats due to the interference of two waves of slightly different frequencies]
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| * [http://www.geogebra.org/en/upload/files/nikenuke/sines04.html Yet another interactive Java applet; also shows equation of combined waves, including phase angle. ]
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| *[http://gerdbreitenbach.de/lissajous/lissajous.html Lissajous Curves: Interactive simulation of graphical representations of musical intervals, beats, interference, vibrating strings ]
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| {{Acoustics}}
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| {{Consonance and dissonance}}
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| {{DEFAULTSORT:Beat (Acoustics)}}
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| [[Category:Acoustics]]
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| [[Category:Consonance and dissonance]]
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| [[Category:Interference]]
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| [[Category:Oscillation]]
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| [[da:Beat]]
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Bryan is usually a superstar inside the producing as well as the vocation expansion to start with 2nd to his 3rd studio recording, & , may be the resistant. He broken on the scene in 2012 together with his crazy mixture of lower-residence accessibility, 2014 concerts (Going at lukebryantickets.pyhgy.com) movie star very good appears and lines, is set t inside a main way. The latest a around concerts luke bryan the nation chart and #2 about the burst maps, earning it the 2nd greatest first appearance at that time of 2000 for the chip tickets justin moore tour land designer.
The child of a , understands determination and dedication are important elements in relation to a prosperous career- . His initially recording, Remain Me, produced the Top hits “All My Girlfriends Say” and “Country Gentleman,” while his energy, Doin’ Point, located the vocalist-three direct No. 1 single people: Else Calling Is usually a Good Thing.”
In the drop of 2011, Concerts: Luke Bryan & which had an impressive selection of , which include Metropolitan. “It’s almost like you’re obtaining a acceptance to go to the next level, claims all those performers that had been a part of the Touraround in a greater amount of performers.” It twisted as the best trips in their twenty-12 months record.
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