2811.29 The general solution to the wave equation (Equation 11.6.10) that yields a standing wave of any arbitrary shape can be obtained as a linear combination of standing sine waves of a form given by Equation 11.6.14, i.e., ()12( , )sincossinnnn nnnxyxtAt Btπωωλ∞==+∑where 2nnTω=since the speed of a wave is … 1202nnnnFvTλωλµ===we have … 1202nnF=But the wavelength of the standing wave is constrained by the fixed endpoints of the string, i.e. … 2nln=, so … 120nFnl=Now, at t = 0, the wave starts from rest in the configuration specified, so…
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.