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On Wikipedia, the general solution for the one-dimensional wave equation is written as u(x,t) = F(x - ct) + G(x + ct).

I don’t see the connection between this solution and what I understand waves to be. Don’t waves need to by cyclical? This general solution doesn’t seem to require the functions to be periodic or cyclical in any sense. What would be a good description of a wave according to the wave equation?