(a) Show that the equations (i) \(A \cos (k x+\omega t)\), (ii) \(e^{-b|x-a t|^{2}}\), and \((i i i)-\left(b^{2} t-x\right)^{2}\) all satisfy the wave equation (Eq. 16. 51) provided that \(A, k, \omega, b\), and \(q\) are constants.

(b) Calculate the speed of each wave of part \(a\).

Data from Eq. 16. 51

Transcribed Image Text:

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