位相変位、位相変化

WordNet

use a shift key on a keyboard; "She could not shift so all her letters are written in lower case"
the time period during which you are at work (同)work shift, duty period
the act of moving from one place to another; "his constant shifting disrupted the class" (同)shifting
an event in which something is displaced without rotation (同)displacement
a crew of workers who work for a specific period of time
change place or direction; "Shift ones position" (同)dislodge, reposition
change gears; "you have to shift when you go down a steep hill"
change in quality; "His tone shifted"
change phonetically as part of a systematic historical change; "Grimm showed how the consonants shifted"
move and exchange for another; "shift the date for our class reunion"
move from one setting or context to another; "shift the emphasis"; "shift ones attention"
arrange in phases or stages; "phase a withdrawal"
(physical chemistry) a distinct state of matter in a system; matter that is identical in chemical composition and physical state and separated from other material by the phase boundary; "the reaction occurs in the liquid phase of the system" (同)form
a particular point in the time of a cycle; measured from some arbitrary zero and expressed as an angle (同)phase_angle
any distinct time period in a sequence of events; "we are in a transitional stage in which many former ideas must be revised or rejected" (同)stage
adjust so as to be in a synchronized condition; "he phased the intake with the output of the machine"
(astronomy) the particular appearance of a bodys state of illumination (especially one of the recurring shapes of the part of Earths moon that is illuminated by the sun); "the full phase of the moon"
continuously varying; "taffeta with shifting colors"
changing position or direction; "he drifted into the shifting crowd"; "their nervous shifting glances"; "shifty winds" (同)shifty
(of soil) unstable; "shifting sands"; "unfirm earth" (同)unfirm

PrepTutorEJDIC

〈人・場所・位置など〉‘を'『移し替える』,置き換える / …‘を'変える,取り替える / 〈自動車のギヤ〉‘を'入れ変える / (…へ)『変わる』,移る《+『to』+『名』》 / 車のギヤを変える;〈車が〉ギヤが入れ変わる・『変換』,転換;移動 / (仕事、作業の)『交替』,交替製;交替の組(人);交替時間 / (特に,自動車)変速装置 / やりくり[算段],一時しのぎの手段,便法;ずるい手段,策略 / シフトドレス(肩から腰までまっすぐした線のゆったりしたワンピース);スリップ
(変化・発達の)『段階』,『局面』 / (物事の)『面』,様相《+『of』+『名』》 / (月・惑星などの)相 / …‘を'段階的に調整(整理)する

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/01/04 07:44:08」(JST)

wiki en

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 and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin.^[1]

Formula

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

\begin{align} x(t) &= A\cdot \cos( 2 \pi f t + \varphi ) \\ y(t) &= A\cdot \sin( 2 \pi f t + \varphi ) = A\cdot \cos\left( 2 \pi f t + \varphi - \tfrac{\pi}{2}\right) \end{align}

where , , and are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period , and they are identical except for a displacement of along the axis. The term phase can refer to several different things:

It can refer to a specified reference, such as , in which case we would say the phase of is , and the phase of is .
It can refer to , in which case we would say and have the same phase but are relative to their own specific references.
In the context of communication waveforms, the time-variant angle , or its principal value, is referred to as instantaneous phase, often just phase.

Phase shift

Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.

Phase shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities.^[1]

is sometimes referred to as a phase shift or phase offset, because it represents a "shift" from zero phase.

For infinitely long sinusoids, a change in is the same as a shift in time, such as a time delay. If is delayed (time-shifted) by of its cycle, it becomes:

\begin{align} x\left(t - \tfrac{1}{4} T\right) &= A\cdot \cos\left(2 \pi f \left(t - \tfrac{1}{4}T \right) + \varphi \right) \\ &= A\cdot \cos\left(2 \pi f t - \tfrac{\pi}{2} + \varphi \right) \end{align}

whose "phase" is now . It has been shifted by radians.

Phase difference

In-phase waves

Out-of-phase waves

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 away from material interfaces and would add increasing distortions with distance.).

Phase difference is the difference, expressed in degrees or time, between two waves having the same frequency and referenced to the same point in time.^[1] 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 degrees from 0° to 360°, or in radians 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 waves meet at a point where they are in antiphase, then destructive 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.

Time is sometimes used (instead of angle) to express position within the cycle of an oscillation. 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.

Time zones are also analogous to phase differences.

A real-world example of a sonic phase difference occurs in the warble of a Native American flute. The amplitude of different harmonic components of same long-held note on the flute come into dominance at different points in the phase cycle. The phase difference between the different harmonics can be observed on a spectrogram of the sound of a warbling flute.^[2]

References

^ ^a ^b ^c Ballou, Glen (2005). Handbook for sound engineers (3 ed.). Focal Press, Gulf Professional Publishing. p. 1499. ISBN 0-240-80758-8.
^ Clint Goss; Barry Higgins (2013). "The Warble". Flutopedia. Retrieved 2013-03-06.

External links

Relationship of phase difference and time-delay
Phase angle, phase difference, time delay, and frequency
ECE 209: Sources of Phase Shift — Discusses the time-domain sources of phase shift in simple linear time-invariant circuits.
Phase Difference Java Applet

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