“wave equation”的概念、定义、翻译、参考文献-科学参考

wave equation

Physics

A partial differential equation of the form:

$\nabla^{2} u = (1 / c^{2}) \partial^{2} u / \partial t^{2}$

where

$\nabla^{2} = \partial^{2} / \partial x^{2} + \partial^{2} / \partial y^{2} + \partial^{2} / \partial z^{2}$

is the Laplace operator (see Laplace equation). It represents the propagation of a wave, where u is the displacement and c the speed of propagation. See also Schrödinger equation.

Mathematics

The hyperbolic partial differential equation ∂²y/∂t² = c²∂²y/∂t² satisfied by small transverse vibrations of a string, where c is the speed of a wave’s propagation, and first studied by d’Alembert. The general solution is y(x,t) = f(x + ct) + g(x−ct), where f and g are arbitrary functions. The wave equation generalizes to three spatial dimensions as ∂²f/∂t² = c²∇²f, as would be satisfied by the electric field of a light wave E(x,t) = A cos (ω‎t−u.x/c), where ω‎ denotes frequency and u is a unit vector parallel to the direction of the wave.

Chemistry

A partial differential equation of the form:
$\nabla^{2} u = (1 / c^{2}) \partial^{2} u / \partial t^{2},$
where
$\nabla^{2} = \partial^{2} / \partial x^{2} + \partial^{2} / \partial y^{2} + \partial^{2} / \partial z^{2}$
is the Laplace operator. It represents the propagation of a wave, where u is the displacement and c the speed of propagation. See also Schrödinger equation.

Electronics and Electrical Engineering

See quantum mechanics.

Geology and Earth Sciences

An equation of wave mechanics which represents wave displacement (ψ‎) and wave velocity (v) as a function of space and time (t), where space can be represented by rectangular coordinates (x, y, z), such that: v²ψ‎ = (δ‎²ψ‎/δ‎x²) + δ‎²ψ‎/δ‎y² + δ‎²ψ‎/δ‎z² = (1/v²)δ‎²ψ‎/δ‎t²; or the equation can be represented in spherical coordinates, such that: (1/v²)δ‎²ψ‎/δ‎t² = (1/r²) [δ‎(r²δ‎ψ‎/r)δ‎r + (1/sin θ‎)(δ‎(sin θ‎ × δ‎ψ‎/δ‎Φ‎)δ‎θ‎) + (1/sin² θ‎)(δ‎²ψ‎/δ‎θ‎²)], where r is the radius, θ‎ the colatitudes, and Φ‎ the longitude.

单词	wave equation
释义	wave equation Physics A partial differential equation of the form: $\nabla^{2} u = (1 / c^{2}) \partial^{2} u / \partial t^{2}$ where $\nabla^{2} = \partial^{2} / \partial x^{2} + \partial^{2} / \partial y^{2} + \partial^{2} / \partial z^{2}$ is the Laplace operator (see Laplace equation). It represents the propagation of a wave, where u is the displacement and c the speed of propagation. See also Schrödinger equation. Mathematics The hyperbolic partial differential equation ∂²y/∂t² = c²∂²y/∂t² satisfied by small transverse vibrations of a string, where c is the speed of a wave’s propagation, and first studied by d’Alembert. The general solution is y(x,t) = f(x + ct) + g(x−ct), where f and g are arbitrary functions. The wave equation generalizes to three spatial dimensions as ∂²f/∂t² = c²∇²f, as would be satisfied by the electric field of a light wave E(x,t) = A cos (ω‎t−u.x/c), where ω‎ denotes frequency and u is a unit vector parallel to the direction of the wave. Chemistry A partial differential equation of the form: $\nabla^{2} u = (1 / c^{2}) \partial^{2} u / \partial t^{2},$ where $\nabla^{2} = \partial^{2} / \partial x^{2} + \partial^{2} / \partial y^{2} + \partial^{2} / \partial z^{2}$ is the Laplace operator. It represents the propagation of a wave, where u is the displacement and c the speed of propagation. See also Schrödinger equation. Electronics and Electrical Engineering See quantum mechanics. Geology and Earth Sciences An equation of wave mechanics which represents wave displacement (ψ‎) and wave velocity (v) as a function of space and time (t), where space can be represented by rectangular coordinates (x, y, z), such that: v²ψ‎ = (δ‎²ψ‎/δ‎x²) + δ‎²ψ‎/δ‎y² + δ‎²ψ‎/δ‎z² = (1/v²)δ‎²ψ‎/δ‎t²; or the equation can be represented in spherical coordinates, such that: (1/v²)δ‎²ψ‎/δ‎t² = (1/r²) [δ‎(r²δ‎ψ‎/r)δ‎r + (1/sin θ‎)(δ‎(sin θ‎ × δ‎ψ‎/δ‎Φ‎)δ‎θ‎) + (1/sin² θ‎)(δ‎²ψ‎/δ‎θ‎²)], where r is the radius, θ‎ the colatitudes, and Φ‎ the longitude.
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