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| {{About|resonance in physics}}
| | == New Balance Wandelschoenen "Like Ik hou van jou" == |
| {{Redirect|Resonant|the phonological term|Sonorant}}
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| [[File:Resonance.PNG|thumb|460px|Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven [[damping|damped]] [[simple harmonic oscillator]].<ref>{{cite book | author = Katsuhiko Ogata | title = System Dynamics | edition = 4th | publisher = University of Minnesota | year = 2005 | page = 617 }}</ref><ref>{{cite book | title = Optics, 3E | author = [[Ajoy Ghatak]] | edition = 3rd | publisher = Tata McGraw-Hill | year = 2005 | isbn = 978-0-07-058583-6 | page = 6.10 | url = http://books.google.com/books?id=jStDc2LmU5IC&pg=PT97&dq=damping-decreases+resonance+amplitude#v=onepage&q=damping-decreases%20resonance%20amplitude&f=false
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| In [[physics]], '''resonance''' is the tendency of a system to [[oscillate]] with greater [[amplitude]] at some [[Frequency|frequencies]] than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's '''resonant frequencies''', or '''resonance frequencies'''. At these frequencies, even small [[Periodic function|periodic]] driving forces can produce large amplitude oscillations, because the system stores [[vibrational energy]].
| | be as specific as you know how<br><br>Ik soort van dacht twee 65s zou een kans hebben, tot en [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=92 New Balance Wandelschoenen] met 10 onder par. Het moet gezegd worden in dit stadium dat Flash gebaseerde sites hebben de neiging om als een van de ergste voor this.6. Het is altijd gemakkelijk om de EASY ding te doen, we leren je om niet te doen wat eenvoudig en in plaats daarvan is, doen wat goed is! U zult verrast zijn, hoeveel mensen zullen je volgen als je opkomen voor wat goed en eervol is EN, vergeven die fouten hebben gemaakt in hun jeugd is het juiste ding om te doen! . <br><br>Een paar dingen die ik heb die hulp gevonden: A) Ik plaats mijn beugel op het dashboard van mijn auto toen het zonnig uit. "Ik hield van hem als een keeper de jaren heen. Dat deel van het zijn sterk. Ik ben het met u eens dat er een argument voor een strenger immigratiebeleid, maar mensen soms meng dat [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=100 New Balance Schoenen Heren] met een algemene afkeer tegenover immigranten. Joe voorspelt dat cloud computing is ingesteld op mainstream computing, periode geworden. In het originele verhaal, Irene Adler is een avonturierster die Holmes outwits, in Sherlock, zoals Jones het uitdrukte: "Ze is uitgegroeid tot een high class dominatrix alleen gered van een wisse dood door [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=3 New Balance Hardloopschoenen 1080] de dramatische tussenkomst van onze held." . <br><br>Zon, 8 december 2013 05:52:00. Was op playoff teams in Tampa Bay (2008), Cincinnati (2010), en Oakland (2012). Families vellen over de traditie van het kijken naar games bij elkaar van generatie op generatie. Als je in de supermarkt, halen haar favoriete ijs. Hij in première zijn eerste single, "Like Ik hou van jou", een schaars dance track geproduceerd door The Neptunes. [27] Het nummer bereikte 11 in de Billboard Hot 100. <br><br>Het jaar daarvoor wonnen ze brons, zodat we zeker op zoek naar medaille en ik denk dat we gaan met de mentaliteit van het winnen van goud, toegevoegd Hicketts, die de geschiedenis van het evenement, dat begon in 1986 heeft bestudeerd. Misra plannen op het team te spelen. Ik kwam erachter dat Amy heeft een ex-vriendje met wie ze kennelijk nog steeds praat, maar ik hoor altijd haar zeggen dat ze single.Thank u voor uw coaching en punt van view.Selwyn die haar outDoc Love's ResponseHi Selwyn kunnen achterhalen, werd je eerste fout besteding . <br><br>Lackey heeft gepost negen kwaliteit begint in zijn laatste 10 voor een 2.30 ERA en heeft slechts vijf over zijn laatste zeven starts liepen. Zelfs [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=77 New Balance Amsterdam] 'Jake the Snake' [Senator Jacob K. Nightmare Ik heb nog deze vliegen in elke serieuze gevecht, maar ik heb een aantal testen gedaan en de tank is heel mooi, condensator kon verbeteringen gebruiken en de kanonnen weer kon krachtiger zijn zonder .<ul> |
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| Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum). However, there are some losses from cycle to cycle, called [[damping]]. When damping is small, the resonant frequency is approximately equal to the [[natural frequency]] of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.
| | <li>[http://www.yaocq.com/news/html/?367945.html http://www.yaocq.com/news/html/?367945.html]</li> |
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| Resonance phenomena occur with all types of vibrations or [[waves]]: there is [[mechanical resonance]], [[acoustic resonance]], [[Electromagnetic radiation|electromagnetic]] resonance, [[nuclear magnetic resonance]] (NMR), [[electron paramagnetic resonance|electron spin resonance]] (ESR) and resonance of quantum [[wave function]]s. Resonant systems can be used to generate vibrations of a specific frequency (e.g., [[musical instrument]]s), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters).
| | <li>[http://www.chantal.cn/bbs/forum.php?mod=viewthread&tid=57465&fromuid=12890 http://www.chantal.cn/bbs/forum.php?mod=viewthread&tid=57465&fromuid=12890]</li> |
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| ==Examples== | | <li>[http://ciarcr.org/spip.php?article310/ http://ciarcr.org/spip.php?article310/]</li> |
| [[File:Little girl on swing.jpg|thumb|280px|Pushing a person in a [[swing (seat)|swing]] is a common example of resonance. The loaded swing, a [[pendulum]], has a [[natural frequency]] of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate.]]
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| | | <li>[http://www.think-group.cn/VK/blog/article.php?type=blog&cid=10&itemid=1712817 http://www.think-group.cn/VK/blog/article.php?type=blog&cid=10&itemid=1712817]</li> |
| One familiar example is a playground [[Swing (seat)|swing]], which acts as a [[pendulum]]. Pushing a person in a swing in time with the natural interval of the swing (its resonant frequency) will make the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo will result in smaller arcs. This is because the energy the swing absorbs is maximized when the pushes are "in [[phase (waves)|phase]]" with the swing's natural oscillations, while some of the swing's energy is actually extracted by the opposing force of the pushes when they are not.
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| | | <li>[http://jz.chy123.com/news/html/?176758.html http://jz.chy123.com/news/html/?176758.html]</li> |
| Resonance occurs widely in nature, and is exploited in many manmade devices. It is the mechanism by which virtually all [[sinusoidal]] [[wave]]s and vibrations are generated. Many sounds we hear, such as when hard objects of [[metal]], [[glass]], or [[wood]] are struck, are caused by brief resonant vibrations in the object. Light and other short wavelength [[electromagnetic radiation]] is produced by resonance on an [[atom]]ic scale, such as [[electron]]s in atoms. Other examples are:
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| * Timekeeping mechanisms of modern clocks and watches, e.g., the [[balance wheel]] in a mechanical [[watch]] and the [[quartz crystal]] in a [[quartz watch]]
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| * [[Tidal resonance]] of the [[Bay of Fundy]]
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| * [[Acoustic resonance]]s of [[musical instruments]] and human [[vocal cords]]
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| * Shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonant frequency)
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| * [[Electrical resonance]] of [[tuned circuit]]s in [[radio]]s and [[TV]]s that allow radio frequencies to be selectively received
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| * Creation of [[Coherence (physics)|coherent]] light by [[optical resonance]] in a [[laser]] [[Optical cavity|cavity]]
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| * [[Orbital resonance]] as exemplified by some [[natural satellite|moons]] of the [[solar system]]'s [[gas giants]]
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| * Material resonances in atomic scale are the basis of several [[spectroscopy|spectroscopic]] techniques that are used in [[condensed matter physics]]
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| **[[Electron spin resonance]]
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| **[[Mössbauer effect]]
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| **[[Nuclear magnetic resonance]]
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| ==Theory==
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| [[File:Universal Resonance Curve.svg|thumb|right|350px|"Universal Resonance Curve", a symmetric approximation to the normalized response of a resonant circuit; [[abscissa]] values are deviation from center frequency, in units of center frequency divided by 2Q; [[ordinate]] is relative amplitude, and phase in cycles; dashed curves compare the range of responses of real two-pole circuits for a Q value of 5; for higher Q values, there is less deviation from the universal curve. Crosses mark the edges of the 3-dB bandwidth (gain 0.707, phase shift 45 degrees or 0.125 cycle).]]
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| The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency, as illustrated for the [[simple harmonic oscillator]] above.
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| For a lightly [[damping|damped]] linear oscillator with a resonance frequency Ω, the ''intensity'' of oscillations ''I'' when the system is driven with a driving frequency ω is typically approximated by a formula that is symmetric about the resonance frequency:<ref>
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| {{cite book
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| | title = Lasers
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| | author = A. E. Siegman
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| | publisher = University Science Books
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| | year = 1986
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| | isbn = 978-0-935702-11-8
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| | pages = 105–108
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| | url = http://books.google.com/books?id=1BZVwUZLTkAC&pg=PA107&dq=resonance-approximation+amplitude+linewidth+frequency+Lorentzian+real#v=onepage&q=resonance-approximation%20amplitude%20linewidth%20frequency%20Lorentzian%20real&f=false
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| }}</ref>
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| : <math>I(\omega) \propto \frac{\left(\frac{\Gamma}{2}\right)^2}{(\omega - \Omega)^2 + \left( \frac{\Gamma}{2} \right)^2 }.</math>
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| The intensity is defined as the square of the amplitude of the oscillations. This is a [[Lorentzian function]], and this response is found in many physical situations involving resonant systems. Γ is a parameter dependent on the [[harmonic oscillator|damping]] of the oscillator, and is known as the ''linewidth'' of the resonance. Heavily damped oscillators tend to have broad linewidths, and respond to a wider range of driving frequencies around the resonant frequency. The linewidth is [[Proportionality (mathematics)|inversely proportional]] to the [[Q factor]], which is a measure of the sharpness of the resonance.
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| In [[electrical engineering]], this approximate symmetric response is known as the ''universal resonance curve'', a concept introduced by [[Frederick E. Terman]] in 1932 to simplify the approximate analysis of radio circuits with a range of center frequencies and Q values.<ref>{{cite book | title = Radio Engineering | author = Frederick Emmons Terman | publisher = McGraw-Hill Book Company | year = 1932 | url = http://books.google.com/books?d=8rE8AAAAIAAJ&q=inauthor:terman+inauthor:frederick+universal&dq=inauthor:terman+inauthor:frederick+universal
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| }}</ref><ref>{{cite book | title = Circuits, Signals, and Systems | author = William McC. Siebert
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| | publisher = MIT Press | year = 1986 | isbn = 978-0-262-19229-3 | page = 113 | url = http://books.google.com/books?id=zBTUiIrb2WIC&pg=PA113&dq=siebert+universal-resonance-curve#v=onepage&q=&f=false
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| }}</ref>
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| ==Resonators==
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| A physical system can have as many resonant frequencies as it has [[degrees of freedom (engineering)|degrees of freedom]]; each degree of freedom can vibrate as a [[harmonic oscillator]]. Systems with one degree of freedom, such as a mass on a spring, [[pendulum]]s, [[balance wheel]]s, and [[RLC circuit|LC tuned circuits]] have one resonant frequency. Systems with two degrees of freedom, such as [[Double pendulum|coupled pendulums]] and [[resonant transformer]]s can have two resonant frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.
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| Extended objects that can experience resonance due to vibrations inside them are called [[resonators]], such as [[organ pipe]]s, [[vibrating string]]s, [[quartz crystal]]s, [[microwave]] cavities, and [[laser]] rods. Since these can be viewed as being made of millions of coupled moving parts (such as [[atom]]s), they can have millions of resonant frequencies. The vibrations inside them travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. If the distance between the sides is <math>d\,</math>, the length of a roundtrip is <math>2d\,</math>. In order to cause resonance, the phase of a [[sinusoidal]] wave after a roundtrip has to be equal to the initial phase, so the waves will reinforce. So the condition for resonance in a resonator is that the roundtrip distance, <math>2d\,</math>, be equal to an [[integer]] number of wavelengths <math>\lambda\,</math> of the wave:
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| :<math>2d = N\lambda,\qquad\qquad N \in \{1,2,3,\dots\}</math>
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| If the velocity of a wave is <math>v\,</math>, the frequency is <math>f = v / \lambda\,</math> so the resonant frequencies are:
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| :<math>f = \frac{Nv}{2d}\qquad\qquad N \in \{1,2,3,\dots\}</math>
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| So the resonant frequencies of resonators, called [[normal modes]], are equally spaced multiples of a lowest frequency called the [[fundamental frequency]]. The multiples are often called [[overtone]]s. There may be several such series of resonant frequencies, corresponding to different modes of vibration.
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| ==Q factor==
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| {{Main|Q factor}}
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| The [[Q factor]] or ''quality factor'' is a [[Dimensionless quantity|dimensionless]] parameter that describes how [[damping|under-damped]] an [[oscillation|oscillator]] or [[resonator]] is,<ref>{{cite book | title = Electric Power Transformer Engineering | author = James H. Harlow | publisher = CRC Press | year = 2004 | isbn = 978-0-8493-1704-0 | pages = 2–216
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| | url = http://books.google.com/books?id=DANXjaoaucYC&pg=PT241&dq=q-factor+damping#v=onepage&q=q-factor%20damping&f=false
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| }}</ref> or equivalently, characterizes a resonator's [[bandwidth (signal processing)|bandwidth]] relative to its center frequency.<ref>{{cite book
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| | title = Electronic Circuits: Fundamentals and Applications | author = Michael H. Tooley | publisher = Newnes | year = 2006 | isbn = 978-0-7506-6923-8
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| | pages = 77–78 | url = http://books.google.com/books?id=8fuppV9O7xwC&pg=PA77&dq=q-factor+bandwidth#v=onepage&q=q-factor%20bandwidth&f=false
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| }}</ref>
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| Higher ''Q'' indicates a lower rate of energy loss relative to the stored energy of the oscillator, i.e., the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high ''Q'', while a pendulum immersed in oil has a low ''Q''. In order to sustain a system in resonance in constant amplitude by providing power externally, the energy that has to be provided within each cycle is less than the energy stored in the system (i.e., the sum of the potential and kinetic) by a factor of <math>Q/(2\pi)</math>. Oscillators with high-quality factors have low [[damping]] which tends to make them ring longer.
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| [[sine wave|Sinusoidally]] driven [[resonator]]s having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around the frequency at which they resonate. The range of frequencies at which the oscillator resonates is called the bandwidth. Thus, a high Q [[RLC circuit|tuned circuit]] in a radio receiver would be more difficult to tune, but would have greater [[selectivity (electronic)|selectivity]], it would do a better job of filtering out signals from other stations that lie nearby on the spectrum. High Q oscillators operate over a smaller range of frequencies and are more stable. (See [[oscillator phase noise]].)
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| The quality factor of oscillators varies substantially from system to system. Systems for which damping is important (such as dampers keeping a door from slamming shut) have ''Q'' = ½. Clocks, lasers, and other systems that need either strong resonance or high frequency stability need high-quality factors. [[Tuning fork]]s have quality factors around ''Q'' = 1000. The quality factor of [[atomic clock]]s and some high-Q [[optical cavity|lasers]] can reach as high as 10<sup>11</sup><ref>[http://www.rp-photonics.com/q_factor.html Encyclopedia of Laser Physics and Technology:Q factor]</ref> and higher.<ref>[http://tf.nist.gov/general/enc-q.htm Time and Frequency from A to Z: Q to Ra]</ref>
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| There are many alternate quantities used by physicists and engineers to describe how damped an oscillator is that are closely related to its quality factor. Important examples include: the [[damping ratio]], [[bandwidth (signal processing)|relative bandwidth]], [[oscillator linewidth|linewidth]], and bandwidth measured in [[Octave (electronics)|octave]]s.
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| ==Types of resonance== | |
| ===Mechanical and acoustic resonance===
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| {{Main|Mechanical resonance|Acoustic resonance|String resonance}}
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| [[Mechanical resonance]] is the tendency of a [[mechanics|mechanical system]] to absorb more energy when the [[frequency]] of its oscillations matches the system's [[natural frequency]] of [[vibration]] than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including [[Bridge engineering|bridges]], buildings, trains, and aircraft. When designing objects, [[engineers]] must ensure the mechanical resonance frequencies of the component parts do not match driving vibrational frequencies of motors or other oscillating parts, a phenomenon known as [[mechanical resonance#Resonance disaster|resonance disaster]].
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| Avoiding resonance disasters is a major concern in every building, tower, and [[bridge]] [[construction]] project. As a countermeasure, [[shock mount]]s can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The [[Taipei 101]] building relies on a {{convert|660|t|ST|adj=mid|[[pendulum]]}}—a [[tuned mass damper]]—to cancel resonance. Furthermore, the structure is designed to resonate at a frequency which does not typically occur. Buildings in [[seismic]] zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition, [[engineer]]s designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.
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| Many [[clock]]s keep time by mechanical resonance in a [[balance wheel]], [[pendulum]], or [[Quartz clock|quartz crystal]]
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| [[Acoustic resonance]] is a branch of [[mechanical resonance]] that is concerned with the mechanical vibrations across the frequency range of human hearing, in other words [[sound]]. For humans, hearing is normally limited to frequencies between about 20 [[Hertz|Hz]] and 20,000 Hz (20 [[kHz]]),<ref>[[Harry F. Olson]] [http://books.google.com/books?id=RUDTFBbb7jAC&pg=PA248 ''Music, Physics and Engineering.''] Dover Publications, 1967, pp. 248–249. "Under very favorable conditions most individuals can obtain tonal characteristics as low as 12 Hz."</ref>
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| Acoustic resonance is an important consideration for instrument builders, as most acoustic [[Musical instrument|instruments]] use [[resonator]]s, such as the [[string resonance|strings]] and body of a [[violin]], the length of tube in a [[flute]], and the shape of, and tension on, a drum membrane.
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| Like mechanical resonance, acoustic resonance can result in catastrophic failure of the object at resonance. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass, although this is difficult in practice.<ref>[http://www.physics.ucla.edu/demoweb/demomanual/acoustics/effects_of_sound/breaking_glass_with_sound.html Breaking Glass with Sound<!-- Bot generated title -->]</ref>
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| ===Electrical resonance===
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| {{Main|Electrical resonance}}
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| [[Electrical resonance]] occurs in an [[electrical network|electric circuit]] at a particular ''resonant frequency'' when the [[Electrical impedance|impedance]] of the circuit is at a minimum in a series circuit or at maximum in a parallel circuit (or when the [[transfer function]] is at a maximum).
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| ===Optical resonance===
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| {{Main|Optical cavity}}
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| An [[optical cavity]], also called an ''optical resonator'', is an arrangement of [[mirror]]s that forms a [[standing wave]] [[cavity resonator]] for [[light wave]]s. Optical cavities are a major component of [[laser]]s, surrounding the [[gain medium]] and providing [[feedback]] of the laser light. They are also used in [[optical parametric oscillator]]s and some [[interferometer]]s. Light confined in the cavity reflects multiple times producing standing waves for certain resonant frequencies. The standing wave patterns produced are called "modes". [[Longitudinal mode]]s differ only in frequency while [[transverse mode]]s differ for different frequencies and have different intensity patterns across the cross-section of the beam. [[Optical ring resonators|Ring resonators]] and [[Whispering gallery|whispering galleries]] are examples of optical resonators that do not form standing waves.
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| Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them; flat mirrors are not often used because of the difficulty of aligning them precisely. The geometry (resonator type) must be chosen so the beam remains stable, i.e., the beam size does not continue to grow with each reflection. Resonator types are also designed to meet other criteria such as minimum beam waist or having no focal point (and therefore intense light at that point) inside the cavity.
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| Optical cavities are designed to have a very large [[Q factor]];<ref>[http://www.rp-photonics.com/q_factor.html Encyclopedia of Laser Physics and Technology - Q factor, quality factor, cavity, resonator, oscillator, frequency standards<!-- Bot generated title -->]</ref> a beam will reflect a very large number of times with little [[attenuation]]. Therefore the frequency [[line width]] of the beam is very small compared to the frequency of the laser.
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| Additional optical resonances are [[guided-mode resonance]]s and [[surface plasmon resonance]], which result in anomalous reflection and high evanescent fields at resonance. In this case, the resonant modes are guided modes of a waveguide or surface plasmon modes of a dielectric-metallic interface. These modes are usually excited by a subwavelength grating.
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| ===Orbital resonance===
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| {{Main|Orbital resonance}}
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| In [[celestial mechanics]], an [[orbital resonance]] occurs when two [[orbit]]ing bodies exert a regular, periodic gravitational influence on each other, usually due to their [[orbital period]]s being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of [[Jupiter]]'s moons [[Ganymede (moon)|Ganymede]], [[Europa (moon)|Europa]], and [[Io (moon)|Io]], and the 2:3 resonance between [[Pluto]] and [[Neptune]]. Unstable resonances with [[Saturn]]'s inner moons give rise to gaps in the [[rings of Saturn]]. The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to [[clear the neighborhood]] around their orbits by ejecting nearly everything else around them; this effect is used in the current [[definition of planet|definition of a planet]].
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| === Atomic, particle, and molecular resonance ===
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| {{Main|Nuclear magnetic resonance|Resonance (particle physics)}}
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| [[File:HWB-NMR - 900MHz - 21.2 Tesla.jpg|thumb|right|300px|NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2-[[Tesla (unit)|tesla]] field, the proton resonance is at 900 MHz.]]
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| [[Nuclear magnetic resonance]] (NMR) is the name given to a physical resonance phenomenon involving the observation of specific [[quantum mechanics|quantum mechanical]] [[magnetism|magnetic]] properties of an [[atom]]ic [[atomic nucleus|nucleus]] in the presence of an applied, external magnetic field. Many scientific techniques exploit NMR phenomena to study [[molecular physics]], [[crystallography|crystal]]s, and non-crystalline materials through [[NMR spectroscopy]]. NMR is also routinely used in advanced medical imaging techniques, such as in [[magnetic resonance imaging]] (MRI).
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| All nuclei containing odd numbers of [[nucleon]]s have an intrinsic [[magnetic moment]] and [[angular momentum]]. A key feature of NMR is that the resonant frequency of a particular substance is directly proportional to the strength of the applied magnetic field. It is this feature that is exploited in imaging techniques; if a sample is placed in a non-uniform magnetic field then the resonant frequencies of the sample's nuclei depend on where in the field they are located. Therefore, the particle can be located quite precisely by its resonant frequency.
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| [[Electron paramagnetic resonance]], otherwise known as ''Electron Spin Resonance'' (ESR) is a spectroscopic technique similar to NMR, but uses unpaired electrons instead. Materials for which this can be applied are much more limited since the material needs to both have an unpaired spin and be [[paramagnetic]].
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| The [[Mössbauer effect]] is the resonant and [[recoil]]-free emission and absorption of [[gamma ray]] photons by atoms bound in a solid form.
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| [[Resonance (particle physics)|Resonance in particle physics]] appears in similar circumstances to [[classical physics]] at the level of [[quantum mechanics]] and [[quantum field theory]]. However, they can also be thought of as unstable particles, with the formula above valid if the <math>\Gamma</math> is the [[Particle decay#Decay rate|decay rate]] and <math>\Omega</math> replaced by the particle's mass M. In that case, the formula comes from the particle's [[Propagator (Quantum Theory)|propagator]], with its mass replaced by the [[complex number]] <math>M+i\Gamma</math>. The formula is further related to the particle's [[Particle decay#Decay rate|decay rate]] by the [[optical theorem]].
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| ===Failure of the original Tacoma Narrows Bridge===
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| {{Main|Tacoma Narrows Bridge (1940)}}
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| The dramatically visible, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie", the original [[Tacoma Narrows Bridge (1940)|Tacoma Narrows Bridge]], is misleadingly characterized as an example of resonance phenomenon in certain textbooks. The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated interaction between the bridge and the winds passing through it—a phenomenon known as [[aeroelasticity#Flutter|aeroelastic flutter]], which is a kind of "self-sustaining vibration" as referred to in the nonlinear theory of vibrations. [[Robert H. Scanlan]], father of [[bridge engineering|bridge]] [[aerodynamics]], has written an article about this misunderstanding.<ref>{{cite journal |url=http://www.ketchum.org/billah/Billah-Scanlan.pdf |title=Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks |author=K. Yusuf Billah and Robert H. Scanlan |year=1991 |journal=[[American Journal of Physics]] |volume=59 |issue=2 |pages=118–124 |format=PDF |accessdate=2011-05-29 |bibcode = 1991AmJPh..59..118B |doi = 10.1119/1.16590 }}</ref>
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| {{details|Mechanical resonance}}
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| ===Resonance causing a vibration on the International Space Station===
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| The [[rocket engine]]s for the [[International Space Station]] (ISS) are controlled by [[autopilot]]. Ordinarily the uploaded parameters for controlling the engine control system for the Zvezda module will cause the rocket engines to boost the International Space Station to a higher orbit. The rocket engines are [[hinge]]-mounted, and ordinarily the operation is not noticed by the crew. But on January 14, 2009, the uploaded parameters caused the autopilot to swing the rocket engines in larger and larger oscillations, at a frequency of 0.5 Hz. These oscillations were captured on video, and lasted for 142 seconds.<ref name=oberg>{{cite news|last=Oberg|first=James|title=Shaking on Space Station Rattles NASA|url=http://www.nbcnews.com/id/28998876/#story|newspaper=NBC News|date=4 February 2009}}</ref>
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| ==See also==
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| {{Portal|Electronics|Physics}}
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| {{Wikipedia books|Resonance}}
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| <div class= style="-moz-column-count:2; column-count:2;">
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| * [[Acoustic resonance]]
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| * [[Center frequency]]
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| * [[Cymatics]]
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| * [[Damping]]
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| * [[Driven harmonic motion]]
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| * [[Earthquake engineering]]
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| * [[Electrical resonance]]
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| * [[Formant]]
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| * [[Harmonic oscillator]]
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| * [[Electrical impedance|Impedance]]
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| * [[Limbic resonance]]
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| * [[Nonlinear resonance]]
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| * [[Positive feedback]]
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| * [[Q factor]]
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| * [[Resonance disaster]]
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| * [[Resonator]]
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| * [[Schumann resonance]]
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| * [[Simple harmonic motion]]
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| * [[Stochastic resonance]]
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| * [[Sympathetic string]]
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| * [[Tuned circuit]]
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| * [[Vibration]]
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| </div> | |
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.answers.com/topic/resonance Definition of Resonance] - "The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force whose frequency is equal or very close to the natural undamped frequency of the system."
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| * [http://www.lightandmatter.com/html_books/lm/ch18/ch18.html Resonance] - a chapter from an online textbook
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| * [[Brian Greene|Greene, Brian]], "''[http://www.pbs.org/wgbh/nova/elegant/resonance.html Resonance in strings]''". [[The Elegant Universe]], [[Nova (series)|NOVA]] ([[Public Broadcasting Service|PBS]])
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/rescon.html#c1 Hyperphysics section on resonance concepts]
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| * [http://users.ece.gatech.edu/~mleach/misc/resonance.html Resonance versus resonant] (usage of terms)
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| * [http://www.johnsankey.ca/bottom.html Wood and Air Resonance in a Harpsichord]
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| * [http://www.phy.hk/wiki/englishhtm/StatWave.htm Java applet] demonstrating resonances on a string when the frequency of the driving force is varied
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| * [http://phy.hk/wiki/englishhtm/Resonance.htm Java applet] demonstrating the occurrence of resonance when the driving frequency matches with the natural frequency of an oscillator
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| * [http://www.acoustics.salford.ac.uk/acoustics_info/glass Breaking glass with sound], including high-speed footage of glass breaking
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| [[Category:Antennas (radio)]]
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| [[Category:Control theory| ]]
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| [[Category:Scattering]]
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| [[Category:Waves]]
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