Question: Consider the simplified wave function Assume that w and v are complex quantities and that k is real: w = a + iβ v =

Consider the simplified wave function

Assume that w and v are complex quantities and that k is real: w = a + iβ v = u + iw
Show that the wave is damped in time. Use the fact that k2 = w2/v2 to obtain expressions for a and β in terms of u and w. Find the phase velocity for this case.

V(x, t) = Ae(wt- kx)

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