I am curious about this too and am trying to become better informed. Is the summing up of the intermodulation products referred to above as described in the section "Intermodulation order" located on the Intermodulation Wikipedia page? If not, a pointer to a suitable explanation would be helpful.
So far I only see examples of excessive driver excursion that have been quoted. They are the only places that there truly is a difference. Fs being a great example theoretically but for a midrange nobody will use it to system resonance. What was not stated in the example in post #24o is that the motor itself will also dampen the excursion as soon as there is no input. Rather rapidly depending on the Qts of the system. If it's a low Qts driver the transient response will approach that of the music signals. Back EMF is an amazing part of this motor system no?
I never said there isn't any intermodulation. That isn't even a point of discussion.
This one is by Beranek, although there should be a Ma(x) and Sd(x) in there as well.
The Re is dependent on temperature.
Btw, which is never talked about.
So I really don't understand why people keep saying that.
I said because of the way Sd(x) works, it looks like the IM products don't sum as as bad. Never that there isn't any intermodulation.
By saying that "it's just different", people ignore the question and subject.
So it's becoming rather frustrating at this point why sone people are being so extremely vague, while the problem is so super clear.
Just look at the excursion dependent shapes of all the variables.
Again, compliance isn't relevant in IMD as already being explained and shown earlier, as well as can be seen in the formula here.
Equation: Sd should be in the numerator and not in the denominator. acts the same way as Bl.
You are correct, don't know why this went wrong. The SPL goes up with higher Sd.
Copied directly this from a paper I was reading.
Copied directly this from a paper I was reading.
I'm not entirely sure about that second statement.
For example, there are these publications:
1. Hot Stuff: Loudspeaker Voice-Coil Temperatures
2. Heat Transfer Mechanisms in Loudspeakers: Analysis, Measurement and Design
3. Voice coil temperature in loudspeaker performance
4. Temperature prediction of the voice coil of a moving coil loudspeaker by computer simulation
5. Loudspeaker Voice-Coil Temperature Estimation
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You're not sure if a piece of wire with a certain resistance (Re in this case) heats up when current passes through?
Also known as thermal and power compression?
To clarify, I was referring to the second statement. Have edited my post to make that clearer. Sorry for the confusion.
The "never talked about" refers to home/studio hifi loudspeakers in sense of distortion and performance.
We can talk about BL(x) or Sd(x) all we want, but when people pump out music for a while, Re is totally butchered to begin with.
This is obviously even more true fro PA / sound reinforcement.
So yes, it's talked about on a scientific level, but not one single manufacturer gives information about its thermal performance.
Or in other words, we have no idea of knowing if certain speakers that promise to perform so well, also will hold up when it comes down to thermal performance.
We can take this even a step further, because compliance is also dependent on temperature.
You can find quite some papers on this, but I bet that @Kravchenko_Audio can also tell quite a bit about this as well.
I think this is a more correct way, although I bet that the format being used will really confuse people;
From; Acoustics: Sound Fields and Transducers, by Beranek and Mellow, page 253
Back in 1944, Olson was studying the effects of nonlinearity in loudspeaker suspensions. He published this figure in a paper titled "The Action of a Direct Radiator Loudspeaker with a Non-Linear Cone Suspension System".
nice. that is pretty early. We also read a paper by Cunningham from 1949 that analyses many of the later known nonlinearities including the Bl(i) modulation which is set by L’(x)
note also that as the Thorborg 1995 paper shows we have Mms(x) modualtion too. They speculated that Mms(x) would change in tandem with Sd(x) which could compensate for the Sd(x) variation. However, requires a certain thickness and sensitive of the cone and surround to work
I tell the truth.
The horse is dead. The whip is broken and I am not exactly interested anymore.
You have all made valid points. And they are not really relevant in a properly designed driver used in a conventional manner. PA use, yes. But in PA use there is not even a beginning of caring about the tiny differences you guys have typed about for so long.
This is tied directly to two functions of a drivers action. Neither of which an end user has any possible control over. This is up to the manufacturer. I will say Sd modulation is a silly discussion. Better to chase unequal motor force plus or minus at rest position. This is something that can be addressed. In driver design this can take me the most time. And is why when a client wants a truly high performance driver I turn to an Underhung motor.
You can get an overhung reasonably linear in the motor force. But not perfectly. It a simple fact of the physics involved.
Read that paper cited. If you want it a few of you have it and can share it. There's a lot in there that is truly relevant when you choose a driver.
So when you are looking for drivers where to look at the proper Klippel tests? Voice Coil magazine has a very large driver test repository. They are reasonably independent. No one is truly independent. And the test are reasonably consistent.
https://audioxpress.com/categories/vc-testbench
No use talking about it without providing the source.
No speculation needed.
A part of the mass is function of the surface area. The non-Mmd part to be exact.
So if the Sd changes, the volume of air changes, therefor the mass must change with it.
I have calculated this, but this part is extremely small.
But if we talk in theoretical terms anyway, like we do with Sd(x), we must take this into the equation as well.
I would recommend reading a couple of pages back, this has already been addressed, incl the same source/reference.
edit; let me be not "that lazy guy", sending you into the woods;
https://www.diyaudio.com/community/...l-x-for-mid-ranges.376164/page-7#post-7703832
In that example I am using efficiency instead of sound pressure, but it basically shows the same thing.
I was mostly talking about how the stiffness can change because things heat up
I would like to see this discussion from all angles, and since some people refuse to share any real data, we have to first to some literature research and do some thought experiments.
I do agree with you that there are a lot more practical considerations.