27 Oct
2006
27 Oct
'06
1:43 a.m.
I made this mistake again last thursday - I computed sound amplitude of some kind of omnidirectional source as being r^-2 where r is the distance. However, I believe that it's energy that should be r^-2, therefore amplitude should be r^-1. That's assuming ideal 3-D dispersion (no ceilings and no walls). Is that right?
Exactly right. For that ideal environment, we have the intensity (W/m^2) distributed evenly on the surface of a sphere at radius r. So, since the surface area of the sphere varies as r^2, the intensity falls off at a rate of r^-2. The energy of the wave is (mostly) conserved, it just gets spread out over a larger area.
Chuck