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I just learned how to derive the wave equation and now I have some questions about it. In my physics text (first year) it simply says (without reason) that the solution to the wave equation is y(x,t) = Acos(kx-wt), where A is the amplitude of displacement, k is the wave number and w is the angular frequency. This makes sense and fits the equation, but why isn't the solution y(x,t) = exp(x+ct), where c is the speed of the wave, valid? It doesn't make sense physically because there is no exponential growth in the amplitude of the wave, but does this come in anywhere? Is there any physical significance to this solution?
PS. I have not taken classes in differential equations yet so it might get explained there, but as of right now I don't know the answer.
PS. I have not taken classes in differential equations yet so it might get explained there, but as of right now I don't know the answer.