Question

Problem 6: Consider the wave equation with a dumping term r > 0, Cut-ºu a + rau, = 0, (t, z) & IR2. This corresponds to the vibrations of an infinite string in a medium that resists its motion (e.g., air or water). Let the energy of the string be given by 1 E() F1 / [u?(t, x) + uş(t, x)) dr. -00 Show that E(t) decreases but E(t)e2rt increases, i.e., the string loses energy due to resistance but does so at a rate slower than e-art. (8 points)

Answer 1

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