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Superposition of Waves
Published in Myeongkyu Lee, Optics for Materials Scientists, 2019
Equations 3.27 and 3.31 also hold for a large number of waves once their frequency range is narrow. The resultant wave is characterized both by the phase velocity, the average velocity of the constituent waves, and by the group velocity, which is the velocity of the modulation envelope. The group velocity is sometimes called the signal velocity, because a signal in the form of any modulated wave travels at the group velocity. The group velocity, which determines the speed with which energy or information is transmitted, is usually less than the phase velocity. When light pulses, consisting of a large number of harmonic waves, are transmitted in a dispersive medium, the velocity of the pulses is different from the velocity of the constituent waves. As shown in Section 1.4, the refractive index n of a medium can be less than unity (< 1) at certain frequencies, implying that the speed of light in the medium at that frequency exceeds the speed of light in vacuum. However, this does not contradict the special theory of relativity; no information-carrying signal can travel faster than the speed of light in vacuum. It is to be noted that the refractive index n is defined with respect to the phase (or wave) velocity, which does not carry information. The speed with which any form of signal travels is always less than c.
Uniform Plane Electromagnetic Waves
Published in Branislav M. Notaroš, Conceptual Electromagnetics, 2017
In general, this is the velocity of travel of electromagnetic energy and information carried by an electromagnetic wave through a given medium, and is also often called the energy velocity or signal velocity.
Ground penetrating radar (GPR) applications in concrete pavements
Published in International Journal of Pavement Engineering, 2022
Alireza Joshaghani, Mehran Shokrabadi
From an electrical viewpoint, materials can be classified as either conductor or dielectric. Conductor materials such as copper or aluminum transmit electric current. However, most pavements are composed of dielectric materials that do not conduct electric current but can sustain an electric field. It is extremely desirable to establish conclusions about the conditions of pavements in an analytical manner. The theory of radar wave propagation in solid objects can be simplified for practical structural testing purposes. Comprehensive attention has been given to the understanding of dielectric properties of concrete pavements to develop interpretation features. The electrical properties that govern the propagation of electromagnetic waves in materials are electrical conductivity and dielectric values. Solid information about the dielectric properties of concrete over a wideband of frequencies is required. Dielectric materials refer to non-conducting or semiconducting materials that can store potential energy. Pavement materials are often considered as dielectric materials. Signal velocity is taken to be inversely proportional to the square root of the relative permittivity (ϵr), which ranges from 1.0 (air) to 81 (water). A dielectric constant value shows both electric and magnetic properties, which describe the permittivity and the permeability of materials, respectively (Avelar Lezama 2007). Since the magnetic permeability of materials is not substantial, the magnetic property is not that important.