wave equation

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wave equation 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/v22Ψ/δt2; or the equation can be represented in spherical coordinates, such that: (1/v22Ψ/δt2 = (1/r2)[δ(r2δΨ/δrr + (1/sin θ)(δ(sin θ × δΨ/δΦ)δθ) + (1/sin2 θ) (δ2Ψ/δθ2)], where r is the radius, θ the colatitude, and Φ the longitude.