On Fri, Jun 17, 2011 at 12:48 PM, Fons Adriaensen <fons@linuxaudio.org> wrote:

For a real single sound source the direction of the
vector V(t) is that towards the source, and P(t) and
V(t) in any given point are closely related. They are
of course measured in different units (Pascal, and
meters/second resp.), one is a scalar and the other
a vector, but they are proportional.

This doesn't matter to the rest of your analysis/description, but I'd offer a correction to this paragraph.

V(x,t) is proportional to the spatial gradient of P(x,t).

Note that this means pressure and velocity waves are 90 degrees out of sync with each other.
One clear case this matters is the boundary conditions at walls. The volume velocity goes to 0 at the wall (Dirichlet), but the pressure has the requirement that its 1st derivative is 0 (Neumann).