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Would lots of sounds tend to cancel out?

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My understanding of sound waves is that they are waves of high and low pressure. So if there were a lot of identical sounds, but randomly out of phase, would they tend to cancel each other out, producing no sound at all? Assuming thousands or even millions of sources of these sounds. To me, it seems more intuitive that the more sounds you have the louder it would get, but I also feel like that couldn't happen.

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