[PD] overdriven speaker

[Martin Schied]

  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
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