## Problem with Packed Stadiums and Entropy

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FFFFireball
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Joined: Tue May 29, 2007 8:05 pm UTC

### Problem with Packed Stadiums and Entropy

Sound waves are just fields of compressed and uncompressed matter, and as they travel your ear will sense as the air's density very subtly changes. as well, loudness is attributed to amplitude, the more displacement of air, the louder we hear it.

Now, as anyone who has ever been to a sporting event can attest, the voices of ten thousand people combined with intense acoustical reverbation makes it a very loud place, meaning conversatins have to be screamed and and music player is pretty much unusable. However, if all those ten thousand voices are each immiting distinct, random patterns of high and low pressure air, logic and entropy would seem to predict that the random deviations of pressure among thousands of people would cancel each other out, creating static air as every area of higher pressure would be in the same area as an area of lower pressure from somebody else, and you would hear nothing in the arena. Of course, this is not the case, but I can't figure out why a crowded arena would result in loud volume.

scowdich
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This "canceling-out" of people's voices assumes a few things:
-People speak in musical tones, or in perfectly periodic signals
-All people are saying the same thing
-All people speak at the same pitch
-Everyone in the stadium is equidistant from you

None of these are really, well, true. By the rules of probability, yes, you may, in a million years or so, encounter a split-second event where the multitude of voices in a stadium will cancel. But realistically? Never happen.

EDIT: Also, intro thread or perish.

FFFFireball
Posts: 10
Joined: Tue May 29, 2007 8:05 pm UTC
Im not assuming they will cancel each other out by wave destruction, im going by the logic of 10,000 random emitters of compressed and decompressed matter, since each space has a 50/50 chance of either being compressed or decompressed by one of the speakers, it seems that the odds of a strong net change in any place would be low.

Scarblac
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Joined: Wed Feb 28, 2007 11:39 am UTC
FFFFireball wrote:Im not assuming they will cancel each other out by wave destruction, im going by the logic of 10,000 random emitters of compressed and decompressed matter, since each space has a 50/50 chance of either being compressed or decompressed by one of the speakers, it seems that the odds of a strong net change in any place would be low.

Yes, it's never going to be near being 10,000 times as strong as one person.

Say that the compression that one person causes varies randomly (uniformly) between -1 and 1.

Then the sum of all those random compression is going to have a normal distribution (bell curve), also centered on 0, which a standard deviation 100 times as large (if I recall correctly, very doubtful).

So it's going to be loud white noise.

See http://en.wikipedia.org/wiki/Central_limit_theorem , and try adding 10,000 random numbers between -1 and 1 together, if you want to experiment

mosc
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you're thinking too three dimensionally. The air in any spot is capable of fluctuating at multiple frequencies simultaneously. Your ear can detect these independent of one another and thus multiple sounds can be heard. It's over the time (say a second) that the chunk of air you're thinking of constantly changes which frequency it is mostly responding to.

It's true that things get garbled. This is quite clearly happening. That typical crowd roar is clearly nothing like the sound each individual is making. When they all chant something like say, "Pedro sucks", each person is not saying it at the same time. They are naturally adjusting to what they hear which creates kind of a self-fulfilling sync.

You can have some real fun with stadiums by recording different locations and playing them back simultaneously.