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== Physical properties == === Propagation=== Wave propagation is any of the ways in which waves travel. With respect to the direction of the [[oscillation]] relative to the propagation direction, we can distinguish between [[longitudinal wave]] and [[transverse wave]]s. [[Electromagnetic wave]]s propagate in [[vacuum]] as well as in material media. Propagation of other wave types such as sound may occur only in a [[transmission medium]]. ==== Reflection of plane waves in a half-space ==== {{further|Reflection coefficient}} The propagation and reflection of plane waves—e.g. Pressure waves ([[P wave]]) or [[S-wave|Shear waves (SH or SV-waves)]] are phenomena that were first characterized within the field of classical [[seismology]], and are now considered fundamental concepts in modern [[seismic tomography]]. The analytical solution to this problem exists and is well known. The frequency domain solution can be obtained by first finding the [[Helmholtz decomposition]] of the displacement field, which is then substituted into the [[wave equation]]. From here, the [[Wave equation#Plane-wave eigenmodes|plane wave eigenmodes]] can be calculated.{{citation needed|date=May 2023}}{{clarify|Unintelligible to the ordinary reader|date=May 2023}} ==== SV wave propagation ==== [[File:SV wave propagation.gif|thumb|upright=1.4|The propagation of SV-wave in a homogeneous half-space (the horizontal displacement field)]] [[File:SV wave propagation y.gif|thumb|upright=1.4|The propagation of SV-wave in a homogeneous half-space (The vertical displacement field){{clarify|date=May 2023}}]] The analytical solution of SV-wave in a half-space indicates that the plane SV wave reflects back to the domain as a P and SV waves, leaving out special cases. The angle of the reflected SV wave is identical to the incidence wave, while the angle of the reflected P wave is greater than the SV wave. For the same wave frequency, the SV wavelength is smaller than the P wavelength. This fact has been depicted in this animated picture.<ref>The animations are taken from {{cite web | url = https://sites.google.com/a/utexas.edu/babakpoursartip/research | title = Topographic amplification of seismic waves | last = Poursartip | first = Babak | year = 2015 | department = UT Austin | access-date = 2023-02-24 | archive-date = 2017-01-09 | archive-url = https://web.archive.org/web/20170109184014/https://sites.google.com/a/utexas.edu/babakpoursartip/research | url-status = dead }}</ref> ==== P wave propagation ==== Similar to the SV wave, the P incidence, in general, reflects as the P and SV wave. There are some special cases where the regime is different.{{clarify|unintelligible to the ordinary reader|date=May 2023}} === Wave velocity === {{further|Phase velocity|Group velocity|Signal velocity}} [[Image:Seismic wave prop mine.gif|thumb|upright=1.4|[[Seismic wave]] propagation in 2D modelled using [[FDTD]] method in the presence of a landmine]] Wave velocity is a general concept, of various kinds of wave velocities, for a wave's [[phase (waves)|phase]] and [[speed]] concerning energy (and information) propagation. The [[phase velocity]] is given as: <math display="block">v_{\rm p} = \frac{\omega}{k},</math> where: * ''v''<sub>p</sub> is the phase velocity (with SI unit m/s), * ''ω'' is the [[angular frequency]] (with SI unit rad/s), * ''k'' is the [[wavenumber]] (with SI unit rad/m). The phase speed gives you the speed at which a point of constant [[phase (waves)|phase]] of the wave will travel for a discrete frequency. The angular frequency ''ω'' cannot be chosen independently from the wavenumber ''k'', but both are related through the [[dispersion relation]]ship: <math display="block">\omega = \Omega(k).</math> In the special case {{math|1=Ω(''k'') = ''ck''}}, with ''c'' a constant, the waves are called non-dispersive, since all frequencies travel at the same phase speed ''c''. For instance [[electromagnetic wave]]s in [[vacuum]] are non-dispersive. In case of other forms of the dispersion relation, we have dispersive waves. The dispersion relationship depends on the medium through which the waves propagate and on the type of waves (for instance [[electromagnetic wave|electromagnetic]], [[sound wave|sound]] or [[ocean surface wave|water]] waves). The speed at which a resultant [[wave packet]] from a narrow range of frequencies will travel is called the [[group velocity]] and is determined from the [[gradient]] of the [[dispersion relation]]: <math display="block">v_{\rm g} = \frac{\partial \omega}{\partial k}</math> In almost all cases, a wave is mainly a movement of energy through a medium. Most often, the group velocity is the velocity at which the energy moves through this medium. [[File:Light dispersion of a mercury-vapor lamp with a flint glass prism IPNr°0125.jpg|thumb|right|upright|Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism]] Waves exhibit common behaviors under a number of standard situations, for example: === Transmission and media === {{Main|Rectilinear propagation|Transmittance|Transmission medium}} Waves normally move in a straight line (that is, rectilinearly) through a ''[[transmission medium]]''. Such media can be classified into one or more of the following categories: * A ''bounded medium'' if it is finite in extent, otherwise an ''unbounded medium'' * A ''linear medium'' if the amplitudes of different waves at any particular point in the medium can be added * A ''uniform medium'' or ''homogeneous medium'' if its physical properties are unchanged at different locations in space * An ''anisotropic medium'' if one or more of its physical properties differ in one or more directions * An ''isotropic medium'' if its physical properties are the ''same'' in all directions === Absorption === {{Main|Absorption (acoustics)|Absorption (electromagnetic radiation)}} Waves are usually defined in media which allow most or all of a wave's energy to propagate without [[Insertion loss|loss]]. However materials may be characterized as "lossy" if they remove energy from a wave, usually converting it into heat. This is termed "absorption." A material which absorbs a wave's energy, either in transmission or reflection, is characterized by a [[refractive index]] which is [[Complex number|complex]]. The amount of absorption will generally depend on the frequency (wavelength) of the wave, which, for instance, explains why objects may appear colored. === Reflection === {{Main|Reflection (physics)}} When a wave strikes a reflective surface, it changes direction, such that the angle made by the [[incident ray|incident wave]] and line [[perpendicular|normal]] to the surface equals the angle made by the reflected wave and the same normal line. === Refraction === {{Main|Refraction}} [[File:Wave refraction.gif|thumb|right|200 px|Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results]] Refraction is the phenomenon of a wave changing its speed. Mathematically, this means that the size of the [[phase velocity]] changes. Typically, refraction occurs when a wave passes from one [[Transmission medium|medium]] into another. The amount by which a wave is refracted by a material is given by the [[refractive index]] of the material. The directions of incidence and refraction are related to the refractive indices of the two materials by [[Snell's law]]. === Diffraction === {{Main|Diffraction}} A wave exhibits diffraction when it encounters an obstacle that bends the wave or when it spreads after emerging from an opening. Diffraction effects are more pronounced when the size of the obstacle or opening is comparable to the wavelength of the wave. === Interference === {{Main|Wave interference}} [[Image:Two sources interference.gif|right|frame|Identical waves from two sources undergoing [[Interference (wave propagation)|interference]]. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.]] When waves in a linear medium (the usual case) cross each other in a region of space, they do not actually interact with each other, but continue on as if the other one were not present. However at any point ''in'' that region the ''field quantities'' describing those waves add according to the [[superposition principle]]. If the waves are of the same frequency in a fixed [[phase (waves)|phase]] relationship, then there will generally be positions at which the two waves are ''in phase'' and their amplitudes ''add'', and other positions where they are ''out of phase'' and their amplitudes (partially or fully) ''cancel''. This is called an [[Interference (wave propagation)|interference pattern]]. === Polarization === {{Main|Polarization (waves)}} [[File:Circular.Polarization.Circularly.Polarized.Light Circular.Polarizer Creating.Left.Handed.Helix.View.svg|class=skin-invert-image|thumb|left]] The phenomenon of polarization arises when wave motion can occur simultaneously in two [[orthogonal]] directions. [[Transverse wave]]s can be polarized, for instance. When polarization is used as a descriptor without qualification, it usually refers to the special, simple case of [[linear polarization]]. A transverse wave is linearly polarized if it oscillates in only one direction or plane. In the case of linear polarization, it is often useful to add the relative orientation of that plane, perpendicular to the direction of travel, in which the oscillation occurs, such as "horizontal" for instance, if the plane of polarization is parallel to the ground. [[Electromagnetic waves]] propagating in free space, for instance, are transverse; they can be polarized by the use of a [[polarizer|polarizing filter]]. Longitudinal waves, such as sound waves, do not exhibit polarization. For these waves there is only one direction of oscillation, that is, along the direction of travel. === Dispersion === [[File:Light dispersion conceptual waves.gif|thumb|right|270 px|Schematic of light being dispersed by a prism. Click to see animation.]] {{Main|Dispersion relation|Dispersion (optics)|Dispersion (water waves)}} Dispersion is the frequency dependence of the [[refractive index]], a consequence of the atomic nature of materials.<ref name=hecht>{{Cite book |last=Hecht |first=Eugene |title=Optics |date=1998 |publisher=Addison-Wesley |isbn=978-0-201-83887-9 |edition=3 |location=Reading, Mass. Harlow}}</ref>{{rp|67}} A wave undergoes dispersion when either the [[phase velocity]] or the [[group velocity]] depends on the wave frequency. Dispersion is seen by letting white light pass through a [[prism (optics)|prism]], the result of which is to produce the spectrum of colors of the rainbow. [[Isaac Newton]] was the first to recognize that this meant that white light was a mixture of light of different colors.<ref name=hecht/>{{rp|190}} === Doppler effect === {{main|Doppler effect}} 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.<ref name="Giordano">{{cite book | last1 = Giordano | first1 = Nicholas | title = College Physics: Reasoning and Relationships | publisher = Cengage Learning | date = 2009 | pages = 421–424 | url = https://books.google.com/books?id=BwistUlpZ7cC&pg=PA424 | isbn = 978-0534424718 }}</ref> It is named after the [[Austria]]n physicist [[Christian Doppler]], who described the phenomenon in 1842.
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