Phase (waves) in the context of Sine

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). For a modulated wave, wavelength may refer to the carrier wavelength of the signal. The term wavelength may also apply to the repeating envelope of modulated waves or waves formed by interference of several sinusoids.

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

In physics, the wavefront of a time-varying wave field is the set (locus) of all points having the same phase. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency (otherwise the phase is not well defined).

Wavefronts usually move with time. For waves propagating in a unidimensional medium, the wavefronts are usually single points; they are curves in a two dimensional medium, and surfaces in a three-dimensional one.

Orcus (minor-planet designation: 90482 Orcus) is a dwarf planet located in the Kuiper belt, with one large moon, Vanth. It has an estimated diameter of 870 to 960 km (540 to 600 mi), comparable to the Inner Solar System dwarf planet Ceres. The surface of Orcus is relatively bright with albedo reaching 23 percent, neutral in color, and rich in water ice. The ice is predominantly in crystalline form, which may be related to past cryovolcanic activity. Other compounds like methane or ammonia may also be present on its surface. Orcus was discovered by American astronomers Michael Brown, Chad Trujillo, and David Rabinowitz on 17 February 2004.

Orcus is a plutino, a trans-Neptunian object that is locked in a 2:3 orbital resonance with the ice giant Neptune, making two revolutions around the Sun to every three of Neptune's. This is much like Pluto, except that the phase of Orcus's orbit is opposite to Pluto's: Orcus is at aphelion (most recently in 2019) around when Pluto is at perihelion (most recently in 1989) and vice versa. Orcus is the second-largest known plutino, after Pluto itself. The perihelion of Orcus's orbit is around 120° from that of Pluto, while the eccentricities and inclinations are similar. Because of these similarities and contrasts, along with its large moon Vanth that can be compared to Pluto's large moon Charon, Orcus has been dubbed the "anti-Pluto". This was a major consideration in selecting its name, as the deity Orcus was the Roman/Etruscan equivalent of the Roman/Greek Pluto.

The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude.

Hyperbolic navigation is a class of radio navigation systems in which a navigation receiver instrument is used to determine location based on the difference in timing of radio waves received from radio navigation beacon transmitters.

Such systems rely on the ability of two widely separated stations to broadcast a signal that is highly correlated in time. Typical systems broadcast either short pulses at the same time, or continual signals that are identical in phase. A receiver located at the midpoint between the two stations will receive the signals at the same time or have identical phase, but at any other location the signal from the closer station will be received first or have a different phase.

A circadian clock, or circadian oscillator, also known as one's internal alarm clock is a biochemical oscillator that cycles with a stable phase and is synchronized with solar time.

Such a clock's in vivo period is necessarily almost exactly 24 hours (the earth's current solar day). In most living organisms, internally synchronized circadian clocks make it possible for the organism to anticipate daily environmental changes corresponding with the day–night cycle and adjust its biology and behavior accordingly.

A crest point on a wave is the highest point of the wave. A crest is a point on a surface wave where the displacement of the medium is at a maximum. A trough is the opposite of a crest, so the minimum or lowest point of the wave.

When the crests and troughs of two sine waves of equal amplitude and frequency intersect or collide, while being in phase with each other, the result is called constructive interference and the magnitudes double (above and below the line). When in antiphase – 180° out of phase – the result is destructive interference: the resulting wave is the undisturbed line having zero amplitude.

A sequence of events is isochronous if the events occur regularly, or at equal time intervals. The term isochronous is used in several technical contexts, but usually refers to the primary subject maintaining a constant period or interval (the reciprocal of frequency), despite variations in other measurable factors in the same system. Isochronous timing is a characteristic of a repeating event, whereas synchronous timing refers to the relationship between two or more events.

• In dynamical systems theory, an oscillator is called isochronous if its frequency is independent of its amplitude.
• In horology, a mechanical clock or watch is isochronous if it runs at the same rate regardless of changes in its drive force, so that it keeps correct time as its mainspring unwinds or chain length varies. Isochrony is important in timekeeping devices. Simply put, if a power-providing device (e.g. a spring or weight) provides constant torque to the wheel train, it will be isochronous, since the escapement will experience the same force regardless of how far the weight has dropped or the spring has unwound.
• In electrical power generation, isochronous means that the frequency of the electricity generated is constant under varying load; there is zero generator droop. (See Synchronization (alternating current).)
• In telecommunications, an isochronous signal is one where the time interval separating any two corresponding transitions is equal to the unit interval or to a multiple of the unit interval; but phase is arbitrary and potentially varying.
  • The term is also used in data transmission to describe cases in which corresponding significant instants of two or more sequential signals have a constant phase relationship.
  • Isochronous burst transmission is used when the information-bearer channel rate is higher than the input data signaling rate.
• In the Universal Serial Bus used in computers, isochronous is one of the four data flow types for USB devices (the others being Control, Interrupt and Bulk). It is commonly used for streaming data types such as video or audio sources. Similarly, the IEEE 1394 interface standard, commonly called Firewire, includes support for isochronous streams of audio and video at known constant rates.
• In particle accelerators an isochronous cyclotron is a cyclotron where the field strength increases with radius to compensate for the relativistic increase in mass with speed.
• An isochrone is a contour line of equal time, for instance, in geological layers, tree rings or wave fronts. An isochrone map or diagram shows such contours.
• In linguistics, isochrony is the postulated rhythmic division of time into equal portions by a language.
• In neurology, isochronic tones are regular beats of a single tone used for brainwave entrainment.

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively.Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop where the outcome of a process reinforces the inciting process to build momentum. As such, these forces can exacerbate the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback. Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics.

Mathematically, positive feedback is defined as a positive loop gain around a closed loop of cause and effect.That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger.Positive feedback tends to cause system instability. When the loop gain is positive and above 1, there will typically be exponential growth, increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will typically accelerate towards extreme values, which may damage or destroy the system, or may end with the system latched into a new stable state. Positive feedback may be controlled by signals in the system being filtered, damped, or limited, or it can be cancelled or reduced by adding negative feedback.

A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation. In engineering, signal processing, and mathematics, Fourier analysis decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.

When any two sine waves of the same frequency (but arbitrary phase) are linearly combined, the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the sine and cosine components, respectively.

Amplitude modulation (AM) is a signal modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the instantaneous amplitude of the wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.

AM was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of the 20th century beginning with Roberto Landell de Moura and Reginald Fessenden's radiotelephone experiments in 1900. This original form of AM is sometimes called double-sideband amplitude modulation (DSBAM), because the standard method produces sidebands on either side of the carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly the carrier signal, which improves the ratio of message power to total transmission power, reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium.

The phase velocity of a wave is the speed of any wavefront, a surface of constant phase. This is the velocity at which the phase of any constant-frequency component of the wave travels. For such a spectral component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity of light waves is not a physically meaningful quantity and is not related to information transfer.