Analytical Mech Homework Solutions 191

Analytical Mech Homework Solutions 191 - 28 11.29 The...

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28 11.29 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., () 1 2 ( , ) sin cos sin nnn n n n x yxt A t B t π ωω λ =  =+   where 2 n n T ω = since the speed of a wave is … 1 2 0 2 nn n n F v T λωλ µ == = we have … 1 2 0 2 n n F = But the wavelength of the standing wave is constrained by the fixed endpoints of the string, i.e. … 2 n l n = , so … 1 2 0 n F n l = Now, at t = 0, the wave starts from rest in the configuration specified, so…
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