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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 ...
Definition. A triangle wave of period p that spans the range [0, 1] is defined as where is the floor function. This can be seen to be the absolute value of a shifted sawtooth wave. For a triangle wave spanning the range [−1, 1] the expression becomes. Triangle wave with amplitude = 5, period = 4. A more general equation for a triangle wave ...
Then the vector =, called the scattering vector or transferred wave vector, measures the difference between the incoming and outgoing wave vectors. The three conditions that the scattering vector Δ k {\displaystyle \mathbf {\Delta k} } must satisfy, called the Laue equations , are the following:
Eikonal approximation. In theoretical physics, the eikonal approximation (Greek εἰκών for likeness, icon or image) is an approximative method useful in wave scattering equations, which occur in optics, seismology, quantum mechanics, quantum electrodynamics, and partial wave expansion.
In the physical theory of diffusion, the Laplace operator arises naturally in the mathematical description of equilibrium. [1] Specifically, if u is the density at equilibrium of some quantity such as a chemical concentration, then the net flux of u through the boundary ∂V (also called S) of any smooth region V is zero, provided there is no source or sink within V: =, where n is the outward ...
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).
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.
Example of voice waveform and its frequency spectrum A periodic waveform (triangle wave) and its frequency spectrum, showing a "fundamental" frequency at 220 Hz followed by multiples (harmonics) of 220 Hz The power spectral density of a segment of music is estimated by two different methods, for comparison