Let's say a sound with power $10^9$ W is produced at an altitude of 20,000 m. Using a simple inverse square law, I calculate that this has sound an intensity of about $10^9 / (4\cdot\pi\cdot20000^2) = 0.2$ W/$\text{m}^2$ (or 113 dB) on the ground.
However, the density of the atmosphere is not constant as the noise makes its way down. We know (see this answer) that sound intensity depends on the air's density here.
Does this mean that the simple inverse square law does not hold for calculating sound intensity through large distances in the atmosphere? Is there a more accurate way to do this?
