I know that a standing wave is the superposition of two waves of equal amplitude and wavelength, moving in opposite directions. But I am looking for a more mathematical defintion of such a wave. The best I can come up with is that (I am foucsing on 1d) its displacement can be written as: $$y=f(x)g(t)$$ But I am not sure if this is right? If not can you please provide me with a mathematical defintion (along with a source if possible) thanks.
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