# Sound and the Decibel

It all has to do with the area under the waves curve squaring with the amplitude and then the area covered by the wave square-rooted with the diameter on account of the d² component of the formula for the area of a sphere.
Cool.
A sound twice as loud as the last, a Bel, by pressure ratio, has an area under its curve 10 times that of the last. The square root of 10 is 3.16 meaning the pressure ratio has to increase by 3.16 in order that the sound becomes twice as loud as the last.
To increase the area under the curve by 10 we have to have 10 identical sound sources. So one sound source becomes twice as loud, or increases by 10 decibels or 1 Bel or ten 10ths of twice as loud, when we stand 10 identical sound sources together.
Two identical sound sources double the area under the curve. This means each dimension of the two area dimensions of the curve increase by square-root 2 which is 1.414, this means the pressure ratio increases by 1.414. Doubling the area under the curve increases the sound pressure level by 3dB
Sound pressure and sound pressure level are not the same thing...
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