Front velocity

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In physics, front velocity is the speed at which the first rise of a pulse above zero moves forward.

In mathematics, it is used to describe the velocity of a propagating front in the solution of hyperbolic partial differential equation.

Various velocities

Associated with propagation of a disturbance are several different velocities. [1] For definiteness, consider an amplitude modulated electromagnetic carrier wave. The phase velocity is the speed of the underlying carrier wave. The group velocity is the speed of the modulation or envelope. Initially it was thought that the group velocity coincided with the speed at which information traveled. However, it turns out that this speed can exceed the speed of light in some circumstances, causing confusion by an apparent conflict with the theory of relativity. That observation led to consideration of what constitutes a signal.

By definition, a signal involves new information or an element of 'surprise' that cannot be predicted from the wave motion at an earlier time. [1] One possible form for a signal (at the point of emission) is:

where u(t) is the Heaviside step function. Using such a form for a signal, it can be shown, subject to the (expected) condition that the refractive index of any medium tends to one as the frequency tends to infinity,[ clarification needed ] that the wave discontinuity, called the front, propagates at a speed less than or equal to the speed of light c in any medium. [1] In fact, the earliest appearance of the front of an electromagnetic disturbance (the precursor) travels at the front velocity, which is c, no matter what the medium. [1] [2] However, the process always starts from zero amplitude and builds up. [2]

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Amplitude modulation Radio modulation via wave amplitude

Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude of the carrier 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.

The Doppler effect or Doppler shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.

Electromagnetic radiation Form of energy emitted and absorbed by particles which are charged which shows wave-like behavior as it travels through space

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays. All of these waves form part of the electromagnetic spectrum.

Frequency Number of occurrences or cycles per unit time

Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency to emphasize the contrast to spatial frequency, and ordinary frequency to emphasize the contrast to angular frequency. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period, T—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Group velocity Physical quantity

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.

Huygens–Fresnel principle Method of analysis

The Huygens–Fresnel principle is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction and also reflection. It states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms the wavefront.

Light Electromagnetic radiation in or near visible spectrum

Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

Optics Branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

Phase velocity

The phase velocity of a wave is the rate at which the wave propagates in some medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as

Refractive index Ratio of the speed of light in vacuum to that in the medium

In optics, the refractive index of a material is a dimensionless number that describes how fast light travels through the material. It is defined as

Speed of light Speed at which all massless particles and associated fields travel in vacuum

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is defined as 299792458 metres per second. It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1299792458 second. According to special relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space.

Wavelength Spatial period of the wave—the distance over which the waves shape repeats, and thus the inverse of the spatial frequency

In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and 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). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Wave Repeated oscillation about a stable equilibrium

In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance of one or more quantities, sometimes as described by a wave equation. In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.

Transverse wave Moving wave whose oscillations are perpendicular to the direction of the wave

In physics, a transverse wave is a wave whose oscillations are perpendicular to the direction of the wave's advance. This is in contrast to a longitudinal wave which travels in the direction of its oscillations.

Dispersion (optics) Dependence of phase velocity on frequency

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity. Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves, and for telecommunication signals along transmission lines or optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption.

In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium.

Slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagation takes place.

The word electricity refers generally to the movement of electrons through a conductor in the presence of a potential difference or an electric field. The speed of this flow has multiple meanings. In everyday electrical and electronic devices, the signals travel as electromagnetic waves typically at 50%–99% of the speed of light, while the electrons themselves move much more slowly, see Drift velocity and Electron mobility.

Lamb waves

Lamb waves propagate in solid plates or spheres. They are elastic waves whose particle motion lies in the plane that contains the direction of wave propagation and the plane normal. In 1917, the English mathematician Horace Lamb published his classic analysis and description of acoustic waves of this type. Their properties turned out to be quite complex. An infinite medium supports just two wave modes traveling at unique velocities; but plates support two infinite sets of Lamb wave modes, whose velocities depend on the relationship between wavelength and plate thickness.

Envelope (waves)

In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable.

References

  1. 1 2 3 4 Peter W. Milonni (2004). Fast light, slow light and left-handed light. CRC Press. pp. 26 ff. ISBN   978-0-7503-0926-4.
  2. 1 2 Julius Adams Stratton (2007). Electromagnetic theory (Classic reissue of 1941 ed.). Wiley/IEEE. p. 337. ISBN   978-0-470-13153-4.