| 释义 |
wave equation 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.
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