[PD] overdriven speaker

[Martin Schied]

  Hi Mathieu -

again, sorry for the big delay. I was a bit busy the past 2 weeks.

On 22.10.2010 07:35, Mathieu Bouchard wrote:
> On Thu, 21 Oct 2010, Martin Schied wrote:
>
>>
>>       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.
>>
>> one could feed the output of this [rpole~] into a [*~] to the input 
>> signal (or at any place later, but then it has to be cared for the 
>> delay of the doppler vd~ too, so better do it first).
>
> Why would you be doing the doppler first ? The heat is generated 
> first, in the moving coil, but the doppler is relative to the 
> observer, who comes at the very end in the data flow from the amp to 
> the ear. Thus it seems to me that the [vd~] should come at the very end.
yes, absolutely...
>
> How does one take the réactance into account, again ?... then we'd 
> have to change the first [*~] to account for ampères not following 
> volts, and do we have to change the other [*~] too ?
I think there are 2 main factors where reactance is important. The first 
is the varying current flow for heat, the second is the varying 
frequency response of the speaker. However I'm not knowing of a 
possibility to model the circuit so you actually have a current and a 
voltage signal. To calculate the heat production the voltage isn't used. 
You have to know the resistance of the coil and the current flowing 
through it. And since the force on the cone relates on the current flow 
(and this is what we hear) and not the voltage we should just not care 
about the voltage and assume the signal in pd is the current signal. Or 
expressed in other words the system should be treated like no difference 
in current and voltage can happen. At least it seems to me this makes a 
lot of things easier and the audibe effects could be estimated. At least 
for me a realistic modeling with verification is out of my knowlegde and 
also my time capabilities are limited at the moment...

>> I think there aren't many too. The only case I can imagine and I 
>> heard of is for huge negative signals, where you can't go beyond 0 
>> pascal of air pressure and the signal is clipped physically - but I 
>> doubt this ever happens in small speakers. Also I'm not sure if this 
>> only happens in compression speakers.
>
> I doubt that it (getting close to 0 pascal) happens at all. It sounds 
> more like a weapon of mass destruction, than like something for 
> listening to.
>
> Though... in some ways, it does happens, at a very small scale. What's 
> the speed of air molecules, and how much time do they take to fill the 
> void made by the speaker moving ? What happens if the speaker moves 
> faster than that ?... (and is that actually the Doppler effect said 
> using different words ?)
That's beyond my knowledge, but I think that's not the point. If you 
calculate the maximum pressure before the negative peak is zero you have 
an spl of approximately 135dB which is not that much for pressure levels 
directly in front of a speaker - possibly I calculated it wrong? I used: 
air pressure: 101.325 Pa and /p/_0 = 20 µPa RMS, which gave me 134.09 dB 
(for a wave with RMS of 101.325 Pa -  so ideally I would have to take 
this as peak level but that doesn't change much, only factor sqrt(2)).
> I don't know what you mean here by «enclosed volume», «free field», 
> nor «radiation resistance».
radiation resistance is the same like impedance, but for mechanical 
systems. You can treat the spring/mass system of the speaker and the air 
similar to an electrical circuit driving an antenna as far as I 
understood. And similar to electrical load you can have pure reactance 
and pure resistance. Unfortunately the internet isn't very wise 
concerning acoustics and speaker systems and is full of voodoo and 
homeopathy instead using the same vocabulary, so I could not find very 
much about it on a quick search.

By enclosed volume I thought of an air tight wooden box with no holes 
other than that for the speaker in it - just like most older 
conventional speakers. Pressing the membrane into the box creates a 
pressure proportional to the excitation of the cone and not anymore to 
the acceleration. I think this closed volume would be called a high 
radiation resistance, because the pressure (analog to the voltage) is 
high for very small air flow (analog to the current).

Martin



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