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Hertz vectors can be advantageous when solving for the electric and magnetic fields in certain scenarios, as they provide an alternative way to define the scalar potential and the vector potential which are used to find the fields as is commonly done.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x component for the x axis) of a vector wave without sources of waves ...
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Wave speed is a wave property, which may refer to absolute value of: . phase velocity, the velocity at which a wave phase propagates at a certain frequency; group velocity, the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for dispersive waves
Sinusoidal plane-wave solutions are particular solutions to the wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations .
A one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity. It contrasts with the second-order two-way wave equation describing a standing wavefield resulting from superposition of two waves in opposite directions (using the squared scalar wave velocity).
The Moens–Korteweg equation states that PWV is proportional to the square root of the incremental elastic modulus, (E inc), of the vessel wall given constant ratio of wall thickness, h, to vessel radius, r, and blood density, ρ, assuming that the artery wall is isotropic and experiences isovolumetric change with pulse pressure.