(Adapted from Serway & Jewett) We stated that a displacement function y(x,t) is a wave if it is a solution to the linear

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Adapted From Serway Jewett We Stated That A Displacement Function Y X T Is A Wave If It Is A Solution To The Linear 1 (102 KiB) Viewed 24 times

(Adapted from Serway & Jewett) We stated that a displacement function y(x,t) is a wave if it is a solution to the linear wave equation: a²y 10²y ax² v² at ² a) (2 pts) Show that the sinusoidal wave function y(x,t) = Asin (kx + wt) is a solution to the linear wave equation, provided that v = w/k. b) (2 pts) Show that the wave function y(x,t) = x² + v²t² is a solution to the wave equation. c) (2 pts) Show that the function in part (b) can be written as f (x + vt) +g(x − vt) and determine the functions fand g. d) (4 pts) Repeat parts (b) and (c) for y(x,t) = sin (x)cos (vt) (Hint: sin (a ± ß) = sin acos ß ± cos asin ß)