# [PD] overdriven speaker

Mathieu Bouchard matju at artengine.ca
Thu Oct 21 06:46:18 CEST 2010

```On Thu, 21 Oct 2010, Martin Schied wrote:

> 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

Alright, I should have thought about it. I mean, it's great that you wrote
it, and it's what was necessary to get me to make a reasoning that would
have been obvious if I were still in grade 13.

> 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...

A simple integrator has a pole at 1. With damping, you use any value a bit
lower than 1. (But you found that already before I finished writing this
mail)

> 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

Isn't the heat proportional to the mean power ? Then you just do [*~] with
itself and then some kind of [rpole~] to account for the accumulation
thereof. After that I don't really know what to do with that.

> or nonlinearities of the air I think.

I don't know them at all. I've never heard of anyone taking them into
account.

> The pressure directly in front of the cone is related to the
> acceleration I think, but I'm not sure about that.

It has to : the speaker makes a sound by pushing and pulling on the air,
and that changes the pressure.

> 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.

It has to... the reason why you hear the sound and why sound has a speed,
is because neighbouring pressure differences cause pressure differences to
propagate. It's a second-order differential equation, as the position of
air particles is proportional to their acceleration. The Laplacian of the
wave function along x,y,z is proportional to the 2nd derivative of the
wave function along t... I'd write it like :

D[D[f,x],x] + D[D[f,y],y] + D[D[f,z],z] = D[D[f,t],t] / v²

Where v² is the square of the speed of sound.

With a slight coordinate change using imaginary numbers, you can see it as
a Laplacian along x,y,z,t instead, in 4-dimensional spacetime, and the
Laplacian is equal to zero. But that's only if the air is considered
frictionless :)

> The power from a 1 kHz sine and a 2 kHz sine are the same anyways, so
> why care...

Ah, that means that the mechanical amplitude (travel) of the wave is much
smaller for treble than bass, is that right ?

_______________________________________________________________________
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
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