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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