Phase (waves)

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.

Formula

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

where $\scriptstyle A\,$ , $\scriptstyle f\,$ , and $\scriptstyle \varphi\,$ are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period $\scriptstyle T = \frac{1}{f}\,$ , and they are identical except for a displacement of $\scriptstyle \frac{T}{4}\,$ along the $\scriptstyle t\,$ axis. The term phase can refer to several different things:

It can refer to a specified reference, such as

\scriptstyle \cos( 2 \pi f t)\,

, in which case we would say the phase of

\scriptstyle x(t)\,

\scriptstyle \varphi\,

, and the phase of

\scriptstyle y(t)\,

\scriptstyle \varphi\,-\, \frac{\pi}{2}\,

It can refer to

\scriptstyle \varphi\,

, in which case we would say

\scriptstyle x(t)\,

and

\scriptstyle y(t)\,

have the same phase but are relative to their own specific references.

In the context of communication waveforms, the time-variant angle

\scriptstyle 2 \pi f t \,+\, \varphi

, or its principal value, is referred to as instantaneous phase, often just phase.

Phase

Phase or phases may refer to:

In science

In physics

Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter—also referred to as a "macroscopic state"

Phase transition is the transformation of a thermodynamic system from one phase to another

Phase transition is the transformation of a thermodynamic system from one phase to another

Phase (separation science)

Mobile phase and Stationary phase in chromatography

Mobile phase and Stationary phase in chromatography

Phase space, a mathematical space in which each possible state of a physical system is represented by a point - this point is also referred to as a "microscopic state"

Phase space formulation, a formulation of quantum mechanics in phase space

Phase space formulation, a formulation of quantum mechanics in phase space

Phase (waves), the initial angle of a sinusoidal function at its origin

Polyphase system, a means of distributing alternating current electric power in multiple conducting wires with definite phase offsets

Single-phase electric power, distribution of AC electric power in a system where the voltages of the supply vary in unison
Three-phase electric power, a common method of AC electric power generation, transmission, and distribution
- Three-phase, the mathematics of three-phase electric power

Waves

Waves are oscillations acompanied by a transfer of energy that travel through space or mass.

Waves may also refer to:

Waves (Charles Lloyd album)

Waves (Jade Warrior album)

Waves, a working title for the Kanye West album The Life of Pablo

Waves (Katrina and the Waves album)

Waves (Moving Mountains album)

Waves (Rhydian Roberts album)

Waves (Sam Rivers album)

Waves (Terje Rypdal album)

Waves (Waves album)

Waves (compilation album), released on the Crydamoure label

Waves II, compilation album released on the Crydamoure label

Waves: Radio 1 Sessions 90–94, a compilation album by Ride

Waves (mixtape), by Mick Jenkins

Waves (Mono Band song)

Waves (Mr Probz song)

Waves (band)

WAVES, the Women Accepted for Volunteer Emergency Service

Waves (festival)

Waves (hairstyle)

Waves, North Carolina

WAVES (New Zealand), a New Zealand anti-vaccination group

[VIDEO]: Discovery Of Ancient Sea Monster Skeleton Has Paleontologists Excited

Edit WorldNews.com 16 Oct 2016

The skeleton of an ancient sea monster discovered more than 50 years ago in Scotland has paleontologists excited over the quantity of bones found and anxious to learn more about the reptile, VOA reported Sunday. Using modern fossil extraction methods, the bones of the sea monster was able to be removed from hard rock. The previously unknown reptile lived in the oceans during the time of the dinosaurs, the report said ... ....

photo: AP / Julio Cortez

Republican presidential candidate Donald Trump is seen on a large screen as he speaks during a charity event hosted by the Republican Hindu Coalition, Saturday, Oct. 15, 2016, in Edison, New Jersey.

Donald Trump Claims Election Will Be Rigged at Polling Sites

Edit Time Magazine 16 Oct 2016

Donald Trump refuses to back down from his claim, which has been made without specific evidence, that the upcoming election results will be rigged at polling places. The Republican nominee for president tweeted on Sunday that the election was being rigged at polling places, just hours after his running mate Gov ... — Donald J. Trump (@realDonaldTrump) October 16, 2016....

photo: US DoS

File - Russian President Vladimir Putin, watched by U.S. Secretary of State John Kerry, U.S. Under Secretary of State for Political Affairs Wendy Sherman, and U.S. Ambasador to Russia John Tefft, urges his guests to take their seat at the Bocherov Ruche - a government villa - in Sochi, Russia, before a bilateral meeting on May 12, 2015.

Putin Hopeful Russia-U.S. Ties Can Be Restored After Elections

Edit Bloomberg 16 Oct 2016

Russia hopes its ties with the U.S. can be restored after elections regardless of who wins, according to President Vladimir Putin. While Democrat Hillary Clinton so far is aggressive toward Russia and Republican Donald Trump wants cooperation, the Kremlin is not ruling out the possibility that the candidates’ positions will change when one of them becomes the U.S ... 16. Photographer ... ....

photo: AP / Khalid Mohammed

Iraq's elite counterterrorism forces gather ahead of an operation to re-take the Islamic State-held City of Mosul, outside Irbil, Iraq, Saturday, Oct. 15, 2016.

Battling horror of ISIS: Iraq's bloody crisis up close

Edit CNN 16 Oct 2016

(CNN)Thousands dead. Millions more driven from their homes. A future far from certain. This is the situation in Iraq today. The deep-rooted sectarian divide that resurfaced amid the chaos of Saddam Hussein's downfall created a security vacuum that ultimately allowed extremist militant groups like ISIS to flourish. READ MORE. High stakes for Iraq's future ... Read More. CNN looks at Iraq's bloody crisis up close.. THE CRISIS IN NUMBERS ... Replay....

photo: NASA / JPL-Caltech/UCLA

File - This image shows the Pleiades cluster of stars as seen through the eyes of WISE, or NASA's Wide-field Infrared Survey Explorer.

Moving beyond the solar system to exoplanets

Edit The Hindu 16 Oct 2016

Ever since the first exoplanet (51 Pegasi b) was discovered in 1995 by Michael Mayor and Didier Queloz, there has been renewed activity and interest in this field. The Kepler and K2 missions of NASA have identified thousands of planet candidates. Now there are nearly 5,000 planet candidates, and of these, some 3,397 have been confirmed as planets, according to the NASA exoplanet archive ... This unit began taking data in 2012 ... ....

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Oral GED-0301 Phase 1b Results Show Clinical Remission and Endoscopic Response at Week 12 in ...

Edit Stockhouse 17 Oct 2016

Oral GED-0301 Phase 1b Results Show Clinical Remission and Endoscopic Response at Week 12 in Patients with Active Crohn’s Disease ... CD-001 is a phase 1b randomized, double-blind, multicenter, exploratory study evaluating the effects of oral GED-0301 on endoscopic and clinical outcomes in patients with active Crohn’s disease ... This treatment phase was followed by an off-treatment observation phase for up to 52 weeks....

Oral GED-0301 Phase 1b Results Show Clinical Remission and Endoscopic Response at Week 12 in Patients with Active Crohn's Disease (Celgene Corporation)

Edit Public Technologies 17 Oct 2016

CELG), today announced that data from a randomized, double-blind, multicenter, exploratory phase 1b study evaluating the effects of investigational oral GED-0301 (mongersen) 160 mg on both endoscopic response and clinical remission in patients with active Crohn's disease will be presented in Vienna, Austria at the United European Gastroenterology Week (UEGW)....

Damaging HFCs to be phased out over next 30 years

Edit Australian Broadcasting Corporation 17 Oct 2016

Over the weekend, more than 170 countries signed an accord in Rwanda that will see the damaging synthetic greenhouse gases usually found in refrigerators and car air conditioners gradually curbed over the next 30 years ... ....

COMMENTARY: President Jokowi’s tax amnesty policy a success story

Edit The Jakarta Post 17 Oct 2016

The first phase of its implementation in the July-September 2016 period showed real success, which really heartened the President ... For that to happen, the period of the next six months (phase two and phase three) should also pay more attention not only to the big companies but also to the SMEs that have not fully participated in this tax amnesty program ... The first phase of the tax amnesty, which ended on Sept....

Trump Organisation claims £150m Turnberry investment

Edit BBC News 17 Oct 2016

"The accounts submitted to Companies House reflect the financial year from 2015 and the first phase of the renovation, which included the clubhouse, the Wee Links pitch and putt and selected function spaces within the hotel ... Ms Malone said it was "nothing short of ridiculous" that it had taken 40 planning applications, 24 planning hearings, a full public inquiry and parliamentary hearing just to build phase one....

Advisory on Multi-Agency Islandwide Counter-Terrorism Exercise (Singapore Police Force)

Edit Public Technologies 17 Oct 2016

(Source. Singapore Police Force) ... The exercise will be conducted in two phases.. Phase. Exercise Date ... 1 ... 2 ... In Phase 1, officers from the SPF and the SAF will be conducting joint patrols at public places such as MRT stations and bus interchanges, while officers from the ICA and the SAF will be conducting joint patrols at the land checkpoints ... In Phase 2, blanks, thunder flashes, and smoke simulators will be used at various locations ... No ... 1 ... 2....

As police step up ID card drive, over 100 migrants leave district

Edit The Hindu 17 Oct 2016

Krishna, Deputy Commissioner of Police, Ernakulam (Law and Order and Traffic), told The Hindu on Sunday that three to four persons in a group of 30 migrant workers were found reluctant to turn up for the registration process after the completion of the first phase of issuing identity cards ... The second phase of providing identity cards to the migrant workers is progressing....

Catherine McKenna proud of 'historic deal' cutting HFC gases to combat climate change

Edit Topix 17 Oct 2016

WATCH ABOVE. Environment Minister Catherine McKenna is calling the climate deal "historic" saying it will phase out HFC's which she said equates to taking 200 million cars off the road each year. A deal was reached Saturday in Kigali , Rwanda, limiting the use of powerful, factory-made greenhouse gases in an effort to fight climate change ... ....

European Mars lander starts descent to Red Planet

Edit Press TV 17 Oct 2016

The test stationary lander’s arrival is only the first phase of the project and its sole job is to pave the way for a rover ...   ....

‘When expectation levels are so high, even 15-minute disruptions hurt badly’

Edit The Hindu 17 Oct 2016

Delhi Metro has emerged as the most comfortable and safe mode of public transport in the city. This, however, is also leading to overcrowding and huge rush during peak hours ... But that doesn’t happen ... Once Phase III is operational, the whole scenario will change ... Phase III will have rings and interchange with a number of lines ... However, after Phase III, there will be bypass lines and one will be able to avoid these central portions ... ....

Funding Metro: Corporates propose, BMRC disposes?

Edit The Times of India 17 Oct 2016

BENGALURU ... But the BMRC's move comes even as companies are actively involved in raising funds ... Agence Francaise de Developement (AFD) has already sanctioned 200 million Euros for Phase II of the project," BMRC MD Pradeep Singh Kharola said ... Box. Developers not keen on funding ... It is said to go through HSR Layout, Agara Junction, Iblur, Bellandur, Marathahalli, Mahadevapura and connect to phase 1 at KR Puram having an interchange station....

Airport runway to be partially closed from Oct. 18

Edit The Hindu 17 Oct 2016

Flight operations at Mumbai airport will be affected from October 18 to November 28 as authorities will be undertaking runway re-carpeting work. This work will be divided in phases, and airlines have been asked to re-schedule their operations as per runway closure timings ... will normalise. ....

Wildcat JV football blasts ’Burg 43-6

Edit Wilmington News Journal 17 Oct 2016

BLANCHESTER — The Blanchester reserve football team defeated Williamsburg 43-6 Saturday. Coach Brian Damewood said the young Wildcats “for the third week in a row … dominated their opponents in all three phases of the game.” ... News Journal Report . ....

Phase (waves)

Formula

Phase

In science

In physics

Waves

See also

Wave Phase

Phase-Aligning a Drum Kit with InPhase: An In-Depth Tutorial

Phase

Wave phase and phase difference

A Level Physics - Wavelength, Period, Amplitude and Phase Difference

Physics Waves part 7 (Phase of Waves - Part 1) CBSE class 11

Sound Waves - Out Of Phase

Physics - Mechanics: Mechanical Waves (6 of 21) Finding Wave Eq. (with Phase Difference)

Live Sound Phase Alignment with the InPhase Plugin

Phase of a Wave

Wave Phase

Phase-Aligning a Drum Kit with InPhase: An In-Depth Tutorial

Phase

Wave phase and phase difference

A Level Physics - Wavelength, Period, Amplitude and Phase Difference

Physics Waves part 7 (Phase of Waves - Part 1) CBSE class 11

Sound Waves - Out Of Phase

Physics - Mechanics: Mechanical Waves (6 of 21) Finding Wave Eq. (with Phase Difference)

Live Sound Phase Alignment with the InPhase Plugin

Phase of a Wave

Wave Phase

Phase-Aligning a Drum Kit with InPhase: An In-Depth Tutorial

Phase

Wave phase and phase difference

A Level Physics - Wavelength, Period, Amplitude and Phase Difference

Physics Waves part 7 (Phase of Waves - Part 1) CBSE class 11

Sound Waves - Out Of Phase

Physics - Mechanics: Mechanical Waves (6 of 21) Finding Wave Eq. (with Phase Difference)

Live Sound Phase Alignment with the InPhase Plugin

Phase of a Wave

Wave Optics: Phase Difference & Path Difference - 03/35

Lec 12: Dispersion, Phase Velocity, Group Velocity | 8.03 Vibrations and Waves (Walter Lewin)

Concept of Wave Packet, Phase & Group Velocity for de Broglie Waves

Standing (Stationary) Waves

8.03 - Lect 12 - Dispersion, Phase Velocity, Group Velocity

8 Hours Relaxing Music | Deep Sleep Music: Alpha Waves | Increase Creativity, Reduce Stress

Waves 2 - Phase, Interference, and Standing Waves (Regents or High School Physics)

Askprojekt - REM Phase (Binaural Beats 5 HZ deep theta waves) Cloud Meditation

Part 3: Wave Propagation and Phase Shifts - G. Jensen

Wave Optics: Phase Difference & Path Difference - 03/35

Lec 12: Dispersion, Phase Velocity, Group Velocity | 8.03 Vibrations and Waves (Walter Lewin)

Concept of Wave Packet, Phase & Group Velocity for de Broglie Waves

Standing (Stationary) Waves

8.03 - Lect 12 - Dispersion, Phase Velocity, Group Velocity

8 Hours Relaxing Music | Deep Sleep Music: Alpha Waves | Increase Creativity, Reduce Stress

Waves 2 - Phase, Interference, and Standing Waves (Regents or High School Physics)

Askprojekt - REM Phase (Binaural Beats 5 HZ deep theta waves) Cloud Meditation

Part 3: Wave Propagation and Phase Shifts - G. Jensen

Wave Phase

Phase-Aligning a Drum Kit with InPhase: An In-Depth Tutorial

Phase

Wave phase and phase difference

A Level Physics - Wavelength, Period, Amplitude and Phase Difference

Physics Waves part 7 (Phase of Waves - Part 1) CBSE class 11

Sound Waves - Out Of Phase

Physics - Mechanics: Mechanical Waves (6 of 21) Finding Wave Eq. (with Phase Difference)

Live Sound Phase Alignment with the InPhase Plugin

Phase of a Wave

Wave Optics: Phase Difference & Path Difference - 03/35

Lec 12: Dispersion, Phase Velocity, Group Velocity | 8.03 Vibrations and Waves (Walter Lewin)

Concept of Wave Packet, Phase & Group Velocity for de Broglie Waves

Standing (Stationary) Waves

8.03 - Lect 12 - Dispersion, Phase Velocity, Group Velocity

8 Hours Relaxing Music | Deep Sleep Music: Alpha Waves | Increase Creativity, Reduce Stress

Waves 2 - Phase, Interference, and Standing Waves (Regents or High School Physics)

Askprojekt - REM Phase (Binaural Beats 5 HZ deep theta waves) Cloud Meditation

Part 3: Wave Propagation and Phase Shifts - G. Jensen

Wave Optics: Phase Difference & Path Difference - ...

Lec 12: Dispersion, Phase Velocity, Group Velocity...

Concept of Wave Packet, Phase & Group Velocity for...

Standing (Stationary) Waves...

8.03 - Lect 12 - Dispersion, Phase Velocity, Group...

8 Hours Relaxing Music | Deep Sleep Music: Alpha W...