Dimensionless variables can be introduced into the wave equation a2uxx = utt in the
Chapter 10, Problem 12(choose chapter or problem)
Dimensionless variables can be introduced into the wave equation a2uxx = utt in the following manner: a. Let s = x/L and show that the wave equation becomes a2uss = L2utt . b. Show that L/a has the dimensions of time and therefore can be used as the unit on the time scale. Let = at/L and show that the wave equation then reduces to uss = u . 13 and 14 indicate the form of the general solution of the wave equation and the physical significance of the constant a.
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