Hi!

Sorry for answering this late. And I was wrong in my last mail. The signal doesn't have to be differentiated but integrated (like you already did in your first post).?

The signal in pd represents the current flowing through the speaker's coil (if we assume it isn't capacitive or inductive load), producing an acceleration equivalent to the current on the speaker cone. The peak output voltage of the amplifier is equal for all frequencies and defines the maximum acceleration the cone can experience. So we can say the acceleration is

a(t)= a_max * -sin(w t)             // w stands for omega = 2 * pi * f, a_max is the (peak) amplitude

If you want to know the speed you have to differentiate it by time:

v(t) = a_max * 1/w * cos(w t)

and for its travel:

x(t) = a_max 1/w² * sin(w t)

so the cone is moving faster for low frequencies (1/f) and also has more travel (1/f²).

It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't - so the 'simulated' cone would just fly away slowly. So some damping should be included in the integrator to make it stable. However I'm no expert on designing filters yet...


Looking at power and air pressure - we don't have to care about them as long as we don't want to include thermal effects or nonlinearities of the air I think. The pressure directly in front of the cone is related to the acceleration I think, but I'm not sure about that. Can anybody confirm that? I think that's not trivial to answer anyways, because already 10cm farther from the speaker the pressure and air velocity are different. The power from a 1 kHz sine and a 2 kHz sine are the same anyways, so  why care...

cheers
Martin