Wave propagation in the context of Eikonal equation


Wave propagation in the context of Eikonal equation

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⭐ Core Definition: Wave propagation

In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling 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.

There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves and string vibrations. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields sustains propagation of waves involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, as determined by their frequencies (or wavelengths), have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.

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Wave propagation in the context of List of natural phenomena

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Wave propagation in the context of Diffraction

Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Diffraction is the same physical effect as interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed.

Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

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Wave propagation in the context of Light absorption

In physics, absorption of electromagnetic radiation is how matter (typically electrons bound in atoms) takes up a photon's energy—and so transforms electromagnetic energy into internal energy of the absorber (for example, thermal energy).

A notable effect of the absorption of electromagnetic radiation is attenuation of the radiation; attenuation is the gradual reduction of the intensity of light waves as they propagate through a medium.

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Wave propagation in the context of Dispersion (optics)

Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.

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, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.

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Wave propagation in the context of Geometrical optics

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.

The simplifying assumptions of geometrical optics include that light rays:

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Wave propagation in the context of Transmission medium

A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate sound, and a transmission medium for sounds may be air, but solids and liquids may also act as the transmission medium. Vacuum or air constitutes a good transmission medium for electromagnetic waves such as light and radio waves. While a material substance is not required for electromagnetic waves to propagate, such waves are usually affected by the transmission medium they pass through, for instance, by absorption or reflection or refraction at the interfaces between media. Technical devices can therefore be employed to transmit or guide waves. Thus, an optical fiber or a copper cable is used as transmission media.

Electromagnetic radiation can be transmitted through an optical medium, such as optical fiber, or through twisted pair wires, coaxial cable, or dielectric-slab waveguides. It may also pass through any physical material that is transparent to the specific wavelength, such as water, air, glass, or concrete. Sound is, by definition, the vibration of matter, so it requires a physical medium for transmission, as do other kinds of mechanical waves and heat energy. Historically, science incorporated various aether theories to explain the transmission medium. However, it is now known that electromagnetic waves do not require a physical transmission medium, and so can travel through the vacuum of free space. Regions of the insulative vacuum can become conductive for electrical conduction through the presence of free electrons, holes, or ions.

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Wave propagation in the context of Huygens–Fresnel principle

The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets and that the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new wavefront. As such, the Huygens–Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.

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Wave propagation in the context of Remote sensing

Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth and other planets. Remote sensing is used in numerous fields, including geophysics, geography, land surveying and most Earth science disciplines (e.g. exploration geophysics, hydrology, ecology, meteorology, oceanography, glaciology, geology). It also has military, intelligence, commercial, economic, planning, and humanitarian applications, among others.

In current usage, the term remote sensing generally refers to the use of satellite- or airborne-based sensor technologies to detect and classify objects on Earth. It includes the surface and the atmosphere and oceans, based on propagated signals (e.g. electromagnetic radiation). It may be split into "active" remote sensing (when a signal is emitted by a sensor mounted on a satellite or aircraft to the object and its reflection is detected by the sensor) and "passive" remote sensing (when the reflection of sunlight is detected by the sensor).

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Wave propagation in the context of Rollin film

A Rollin film, named after Bernard V. Rollin, is a 30 nm-thick liquid film of helium in the helium II state. It exhibits a "creeping" effect in response to surfaces extending past the film's level (wave propagation). Helium II can escape from any non-closed container via creeping toward and eventually evaporating from capillaries of 10 to 100 nm or greater.

Rollin films are involved in the fountain effect where superfluid helium leaks out of a container in a fountain-like manner. They have high thermal conductivity.

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Wave propagation in the context of Phonautograph

The phonautograph is the earliest known device for recording sound. Previously, tracings had been obtained of the sound-producing vibratory motions of tuning forks and other objects by physical contact with them, but not of actual sound waves as they propagated through air or other mediums. Invented by Frenchman Édouard-Léon Scott de Martinville, it was patented on March 25, 1857. It transcribed sound waves as undulations or other deviations in a line traced on smoke-blackened paper or glass. Scott believed that future technology would allow the traces to be deciphered as a kind of "natural stenography". Intended as a laboratory instrument for the study of acoustics, it was used to visually study and measure the amplitude envelopes and waveforms of speech and other sounds or to determine the frequency of a given musical pitch by comparison with a simultaneously recorded reference frequency.

It did not occur to anyone before the 1870s that the recordings, called phonautograms, contained enough information about the sound that they could, in theory, be used to recreate it. Because the phonautogram tracing was an insubstantial two-dimensional line, direct physical playback was impossible in any case. However, several phonautograms recorded before 1861 were successfully converted and played as sound in 2008 by optically scanning them and using a computer to process the scans into digital audio files.

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Wave propagation in the context of Cherenkov radiation

Cherenkov radiation (/əˈrɛŋkɒf/) is an electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov.

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Wave propagation in the context of Transmission coefficient

The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A transmission coefficient describes the amplitude, intensity, or total power of a transmitted wave relative to an incident wave.

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Wave propagation in the context of Line-of-sight propagation

Line-of-sight propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves can only travel in a direct visual path from the source to the receiver without obstacles. Electromagnetic transmission includes light emissions traveling in a straight line. The rays or waves may be diffracted, refracted, reflected, or absorbed by the atmosphere and obstructions with material and generally cannot travel over the horizon or behind obstacles.

In contrast to line-of-sight propagation, at low frequency (below approximately 3 MHz) due to diffraction, radio waves can travel as ground waves, which follow the contour of the Earth. This enables AM radio stations to transmit beyond the horizon. Additionally, frequencies in the shortwave bands between approximately 1 and 30 MHz, can be refracted back to Earth by the ionosphere, called skywave or "skip" propagation, thus giving radio transmissions in this range a potentially global reach.

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Wave propagation in the context of Longitudinal wave

Longitudinal waves are waves which oscillate in the direction which is parallel to the direction in which the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when travelling through a medium, and pressure waves, because they produce increases and decreases in pressure. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P waves (created by earthquakes and explosions).

The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe some bulk sound waves in solid materials (but not in fluids); these are also called "shear waves" to differentiate them from the (longitudinal) pressure waves that these materials also support.

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