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Nothing will happen to the waves unless they hit some kind of reflective boundary. Then the first wave will affect the second wave as it is reflected depending on the frequency of the wave and the wave's velocity. At the point where the waves intersect they can momentarily amplify or negate each other (or any mix in between) depending on their momentary orientation. As the waves travel, there will be a point where each happens in full and there will be an intermediate area between that will be some hybrid. When the waves are continuous such as in a pure tone of sound generated from a speaker, this will create "nodes" of cancellation and amplification that are stationary within a room. This is most notable with low frequencies because of the longer wavelength. However, if the waves never encounter such a reflective surface, they will never affect each other.

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