Why doesnt sound decrease by 12db? Considering omni-directional sound source,why doesnt sound decrease by 12db per doubling of distance?
I read about sound decreasing with distance and everybody claim that sound decrease 6db per doubling of distance,that is in my opinion impossible and completly wrong becose the soundwave will spread 4x in area,it will double in both height and width,that means one fourth or 25%.
I read on site called Sengpiel audio that sound decreases 12db per doubling in near field and them 6db in far field,I also read that sound in near field doesnt decrease at all,instead it fluctuates up and down chaoticaly.
 A: The Sound pressure $p$ decreases with the distance $r$ from the source as:
$p \propto \frac{1}{r}$.
The effective Sound pressure you obtain by computing the time average of the square of the pressure fluctuation $p(t)$ dependent on time $t$, i.e. for the effective Sound pressure it holds
$P = \sqrt {\frac{1}{T} \int_0^T p^2(t)dt}$
for a characteristic time $T$. For fixed distance $r$ you also get $P \propto 1/r$. To get the Sound pressure Level in dB you have to compute
$P_{dB} =20 \log_{10} P$.
The difference in Sound pressure Levels between being at the source at $r$ and being at the source at $2r$ will be
$P_{dB}(2r)-P_{dB}(r) = 20 \log_{10} \frac{K}{2r} - 20 \log_{10} \frac{K}{r} = 20 \log_{10} (\frac{K}{2r}/ \frac{K}{r}) = - 20 \log_{10} 2$
that is exactly 6 dB.
A: You say there is a envelope spread of 4x when distance doubles. That is correct. So the acoustic energy per unit area falls by 4x. This is required for conservation of energy.
The convention with decibel language for energy is 10log(energy) so 4x is 6 dB. 
Sound pressure, mentioned in other responses, is proportional to the square root of the energy (aka amplitude), hence it falls down by a factor of 2. 
Nevertheless, there is no ambiguity in decibel language. For amplitude related factors, the convention is 20log(amplitude), which again is 6 dB.
