Consider the one-dimensional infinite space wave equation with a periodic source of

Chapter 9, Problem 9.3.13

(choose chapter or problem)

Consider the one-dimensional infinite space wave equation with a periodic source of frequency : 2 t2 = c 2 2 x2 + g(x)e it. (9.3.57) (a) Show that a particular solution = u(x)eit of (9.3.57) is obtained if u satisfies a nonhomogeneous Helmholtz equation d2u dx2 + k2u = f(x). *(b) The Greens function G(x, x0) satisfies d2G dx2 + k2G = (x x0). Determine this infinite space Greens function so that the corresponding (x, t) is an outward-propagating wave. (c) Determine a particular solution of (9.3.57).

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