ct) (x ct) (11.4) x ct [f(x ct) f(x ct)] u(x, t) (17.8) C Jr-ct Problem 1 (25 po

Question

ct) (x ct) (11.4) x ct [f(x ct) f(x ct)] u(x, t) (17.8) C Jr-ct Problem 1 (25 points): A spherical wave is a solution of the three-dimensional wave equation of the form u(r,t), where r is the distance to the origin (the spherical coordinate). The wave equation takes the form "spherical wave equation") urr -u (a) Change variables v ru to get the equation for v:vtt c2vrr (b) Solve for v using (17.4) and thereby solve the spherical equation. (c) Use (17.8) to solve it with initial conditions u(r ut(r,0) -r2.

Explanation / Answer

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