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AandNot-A comments on Open Thread, July 16-31, 2012 - Less Wrong
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How exactly is sound additive? I'm having a festival near home (maybe some 2 kilometers away) and I know no individual has the capacity to shout at a volume that reaches my house. But when the 80k people that are watching do it, then it reaches my house. So, how does that happen?
Sounds are waves transmitted by air. Waves can reinforce or cancel each other, but cancelling can only go so far (to zero), so what is left is the sound resulting from the reinforced waves.
Not a real answer.
Sound is measured in Bels. This is a logarithimic scale. 2 Bels is 10 times as loud as 1, 3 ten times as loud as 2, etcetera. Since sound is a wave I expect the intensity to diminish at constant*(inverse square of distance).
Arbitralily say each individual emits 1 unit of sound.
80,000/(2,000^2) = 0.02 Magnitude of arbitrary unit is 0.02 at 2km 80,000 / (1000^2) = 0.08 Magnitude of arbitrary unit is 0.08 at 1km
Basically it's an example of an inverse square law. No real understanding of physics was used in this comment.
This was more specific than I imagined, thank you. The basis intuition should be that dropping two rocks on a pond makes two waves that collapse onto each other and form one bigger wave, right?
I'm not an expert, but here's what I'd guess:
If 100 people stood exactly the same distance from your house, and sang the same pure note in phase with each other, the resulting sound would arrive with an amplitude 100 times greater than if it was just one person.
If 100 people stood at random distances from your house, and sang the same pure note all with different phases, the resulting sound would arrive with an amplitude 10 times greater.
Correct, but misleading. The power is proportional to the square of the amplitude. Also, the people being in phase depends on where you're standing. If you stand in just the right (or rather, wrong) spot, you get 100 times the amplitude and 10,000 times the power, but if you average the power output in all directions, it would end up being 100 times the power.