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| {{merge from|Instantaneous phase|date=September 2013}}
| | Oscar is what my spouse loves to call me and I completely dig that title. South Dakota is where me and my spouse reside. To gather badges is what her family members and her appreciate. For years he's been working as a meter reader and it's some thing he really enjoy.<br><br>my weblog ... [https://singhpreet.com/groups/valuable-guidance-for-successfully-treating-infections/ std testing at home] |
| {{merge from|Phase angle|date=October 2013}}
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| '''Phase''' in [[sinusoidal]] functions or in waves has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its [[Origin (mathematics)|origin]] and is sometimes called '''phase offset''' or '''phase difference'''. Another usage is the fraction of the wave cycle which has elapsed relative to the origin.<ref name=Ballou2005>{{cite book |last=Ballou |first=Glen |title=Handbook for sound engineers |url=http://books.google.com/books?id=y0d9VA0lkogC&pg=PA1499 |edition=3 |year=2005 |publisher=Focal Press, Gulf Professional Publishing |isbn=0-240-80758-8 |page=1499}}</ref>
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| ==Formula==
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| The phase of an [[Simple harmonic motion|oscillation]] or [[Sine wave|wave]] refers to a sinusoidal function such as the following:
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| :<math>\begin{align}
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| x(t) &= A\cdot \cos( 2 \pi f t + \varphi ) \\
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| y(t) &= A\cdot \sin( 2 \pi f t + \varphi ) = A\cdot \cos\left( 2 \pi f t + \varphi - \tfrac{\pi}{2}\right)
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| \end{align}</math>
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| where <math>\scriptstyle A\,</math>, <math>\scriptstyle f\,</math>, and <math>\scriptstyle \varphi\,</math> are constant parameters called the ''amplitude'', ''frequency'', and ''phase'' of the sinusoid. These functions are periodic with period <math>\scriptstyle T = \frac{1}{f}\,</math>, and they are identical except for a displacement of <math>\scriptstyle \frac{T}{4}\,</math> along the <math>\scriptstyle t\,</math> axis. The term '''phase''' can refer to several different things''':''' | |
| *It can refer to a specified reference, such as <math>\scriptstyle \cos( 2 \pi f t)\,</math>, in which case we would say the '''phase''' of <math>\scriptstyle x(t)\,</math> is <math>\scriptstyle \varphi\,</math>, and the '''phase''' of <math>\scriptstyle y(t)\,</math> is <math>\scriptstyle \varphi\,-\, \frac{\pi}{2}\,</math>.
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| *It can refer to <math>\scriptstyle \varphi\,</math>, in which case we would say <math>\scriptstyle x(t)\,</math> and <math>\scriptstyle y(t)\,</math> have the same '''phase''' but are relative to their own specific references.
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| *In the context of communication waveforms, the time-variant angle <math>\scriptstyle 2 \pi f t \,+\, \varphi</math>, or its [[principal value]], is referred to as '''[[instantaneous phase]]''', often just '''phase'''.
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| == Phase shift ==
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| [[Image:Phase shift.svg|thumb|Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.]]
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| '''Phase shift''' is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities.<ref name=Ballou2005/>
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| <math>\scriptstyle \varphi\,</math> is sometimes referred to as a ''phase shift'' or ''phase offset'', because it represents a "shift" from zero phase.
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| For infinitely long sinusoids, a change in <math>\scriptstyle \varphi\,</math> is the same as a shift in time, such as a time delay. If <math>\scriptstyle x(t)\,</math> is delayed (time-shifted) by <math>\scriptstyle \frac{1}{4}\,</math> of its cycle, it becomes:
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| :<math>\begin{align}
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| x\left(t - \tfrac{1}{4} T\right) &= A\cdot \cos\left(2 \pi f \left(t - \tfrac{1}{4}T \right) + \varphi \right) \\
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| &= A\cdot \cos\left(2 \pi f t - \tfrac{\pi}{2} + \varphi \right)
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| \end{align}</math>
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| whose "phase" is now <math>\scriptstyle \varphi \,-\, \frac{\pi}{2}</math>. It has been shifted by <math>\scriptstyle \frac{\pi}{2}</math> radians.
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| == Phase difference {{anchor|Phase difference}} ==
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| [[Image:Sine waves same phase.svg|thumb|In-phase waves]]
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| [[Image:Sine waves different phase.svg|thumb|Out-of-phase waves]]
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| [[Image:Phase-shift illustration.png|right|thumb|Left: the [[real part]] of a [[plane wave]] moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts. (The illustration on the right ignores the effect of [[diffraction]], which would make the waveform [[continuous function|continuous]] away from material interfaces and would add increasing distortions with distance.).]]
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| '''Phase difference''' is the difference, expressed in electrical degrees or time, between two waves having the same frequency and referenced to the same point in time.<ref name=Ballou2005/> Two oscillators that have the same frequency and no phase difference are said to be '''in phase'''. Two oscillators that have the same frequency and different phases have a phase difference, and the oscillators are said to be '''out of phase''' with each other. The amount by which such oscillators are out of phase with each other can be expressed in [[degree (angle)|degree]]s from 0° to 360°, or in [[radian]]s from 0 to 2π. If the phase difference is 180 degrees (π radians), then the two oscillators are said to be in '''antiphase'''. If two interacting [[wave]]s meet at a point where they are in antiphase, then destructive [[Interference (wave propagation)|interference]] will occur. It is common for waves of electromagnetic (light, RF), acoustic (sound) or other energy to become superposed in their transmission medium. When that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes.
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| Time is sometimes used (instead of angle) to express position within the cycle of an oscillation.
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| A phase difference is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time. But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds (different frequencies), the phase difference is undefined and would only reflect different starting positions. Technically, phase difference between two entities at various frequencies is undefined and does not exist.
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| *Time zones are also analogous to phase differences.
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| A real-world example of a sonic phase difference occurs in the [[Native American flute#The Warble|warble of a Native American flute]]. The amplitude of different [[Harmonics|harmonic components]] of same long-held note on the flute come into dominance at different points in the phase cycle.
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| The phase difference between the different harmonics can be observed on a [[spectrograph]] of the sound of a warbling flute.<ref>{{cite web |url=http://Flutopedia.com/warble.htm |title=The Warble |work=Flutopedia |author1=Clint Goss |author2=Barry Higgins |year=2013 |accessdate=2013-03-06}}</ref>
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| == Quantum mechanics ==
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| In physics, [[quantum mechanics]] ascribes waves to physical objects. The [[wave function]] is [[complex number|complex]] and since its square modulus is associated with the probability of observing the object, the complex character of the wave function is associated to the phase. Since the complex algebra is responsible for the striking interference effect of quantum mechanics, phase of particles is therefore ultimately related to their quantum behavior.
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| == See also ==
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| *[[In-phase and quadrature components]]
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| *[[Instantaneous phase]]
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| *[[Lissajous curve]]
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| *[[Phase angle]]
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| *[[Phase cancellation]]
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| *[[Phase problem]]
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| *[[Phase velocity]]
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| *[[Phasor]]
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| *[[Polarity (physics)|Polarity]]
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| *[[Polarization (waves)|Polarization]]
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| *[[coherence (physics)|Coherence]], the quality of a wave to display a well defined phase relationship in different regions of its domain of definition
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| ==References==
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| {{reflist}}
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| ==External links==
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| {{Commons category|Phase (waves)}}
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| *[http://www.kwantlen.ca/science/physics/faculty/mcoombes/P2421_Notes/Phasors/doublesine.gif Relationship of phase difference and time-delay]
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| *[http://www.sengpielaudio.com/calculator-timedelayphase.htm Phase angle, phase difference, time delay, and frequency]
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| *[http://www.tedpavlic.com/teaching/osu/ece209/lab3_opamp_FO/lab3_opamp_FO_phase_shift.pdf ECE 209: Sources of Phase Shift] — Discusses the time-domain sources of phase shift in simple linear time-invariant circuits.
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| *[http://phy.hk/wiki/englishhtm/phase.htm Phase Difference] Java Applet
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| [[Category:Wave mechanics]]
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| [[Category:Physical quantities]]
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Oscar is what my spouse loves to call me and I completely dig that title. South Dakota is where me and my spouse reside. To gather badges is what her family members and her appreciate. For years he's been working as a meter reader and it's some thing he really enjoy.
my weblog ... std testing at home