Question: If f is a scalar function of one scalar variable, we know that f (z ct) are solutions of the one-dimensional wave equation. (a)

If f is a scalar function of one scalar variable, we know that f (z ± ct) are solutions of the one-dimensional wave equation.

(a) Show that f (r ± ct) / r are solutions of the three-dimensional wave equation in spherical coordinates.
(b) Show that f (ρ ± ct) / √ρ are solutions of the two-dimensional wave equation in cylindrical coordinates when ρ is sufficiently large. Make a precise definition of “sufficiently large”.

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a b Let Gr t F r tr There is no angular dependence so G 18 r r ... View full answer

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