The equation for a standing wave on a string with mass density μ is y(x,t) = 2A cos (ωt) sin (kx). Show that the average kinetic energy and potential energy over time for this wave per unit length are given by Kave(x) =μ ω2 A2 sin2 kx and Uave(x) = T(kA)2 (cos2 kx).
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