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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If two different noise signals of equal power are added together, the volume doesn't double, as DC voltages would, but goes up by the square root of two. So yes there is a certain amount of canceling out, but the overall trend is louder.
 
Freespader, Yes, sound waves in fluids like air, for example, are periodic pressure variations. If there are "a lot of identical sounds but (some of them) randomly out of phase" those will cancel out. At the same time there will be other waves in phase and so they would reinforce one another to make the result louder. You are correct: generally speaking, the more sounds present the louder it would be.

We cannot learn how natural mechanisms function intuitively, nor can we understand nature by how we feel about its processes. Sometimes we see experiments that demonstrate counter-intuitive results. Emotions have no place in physics. We have to use the scientific method if we are to arrive at correct understandings.
 
In addition: think about light of different wavelenghts, phases, intensities and directions of propagation. If all wavelenghts have the same probability to be present, the result is white light. In acoustic is called white noise:
http://en.wikipedia.org/wiki/White_noise