Thiele-Small Parameters Question: Cms, Fs

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.
diyAudio Moderator Emeritus
Joined 2001
I'm trying to find out what happens if you take the spider off a speaker and replace it with one softer, less springy.

From the following source, Measuring Loudspeaker Driver Parameters, I got the following information:

Calculate cone mass ...

M = M1 / (( Fs / Fs¹ )² -1 )

Next, determine Cms ...

Cms = 1 / ( 2 * π * fs )² * M (Equation 1)
VAS = CMS * d * c² * A² (Equation 2)
Equations numbered by myself.

A softer spider would have a higher Cms, a stiffer spider would have a lower Cms, (assuming the surrounds are so soft they affect the situation little).

So Equation 2 would indicate, since d, c² and A² aren't changing, we would assume that a spider half as springy would have a Cms twice as high so Vas would double.

However, Equation 1 would indicate that in order to get to that higher Cms value, the softer spider would have to lower fs or more mass would have to be added to the cone. Is that correct?

So in other words, you cannot just substitute the original spider with one half as springy without affecting a Thiele-Small parameter besides Vas.

Am I right on this?

I was playing around with BoxModel below and I was having some problems ascertaining this.
 

Attachments

  • Box Model message.jpg
    Box Model message.jpg
    118.5 KB · Views: 492
Last edited:
diyAudio Moderator Emeritus
Joined 2001
Thank you for your prompt answer.

But, when the softer, less springy spider is substituted for the original, won't Mms or Fs change in order for the spider to get that higher Cms value?

I thought that is what Equation 1 seems to show, (I might well be wrong, I'm not in the field).

Put another way, suppose I substitute a softer spider in a given speaker without changing Bl or Mms. Will Vas get larger and nothing else change? Or will fs or some other Thiele-Small parameter have to change as well?
 
Last edited:
Fs must also change.

I have recently replaced a cambric suspension on a pro 15" driver with a foam surround, Fs reduced from 33Hz to 25Hz. As Fs is squared in this equation:

Cms = 1 / ( 2 * π * fs )² * M (Equation 1)

Cms in my example will have increased by a factor of around 1.74, assuming there is no increase in Mms. So VAS will also follow suit increasing from 184L to 320L. What I don't know is what happens to qe. and qm. I think these parameters will also change, especially qm. yielding a new, possibly lower qts. Also I would expect a driver to lose some power handling with a softer suspension.
 
Also I would expect a driver to lose some power handling with a softer suspension.

That may be relevant at higher frequencies. Excursion is generally what limits output at bass frequencies, not electrical power. That's true unless the woofer is in a tiny box and needs a great deal of power to reach its x-max.

Seems to me, many woofers (especially pro woofers) have excessively low compliance and corresponding low VAS and high Fs. Most likely they do this so you can dump more watts in the voice coil without exceeding mechanical excursion limits. But it reduces efficiency at bass frequencies, so you either need EQ to go deeper, or get limited bass depth.
 
Hi,

Driver Qts will change in the same way its changed by a box, in this
case lower Fs and higher Vas will mean a lower free air driver Qts.

i.e. for a driver with Qts of 0.5 halving Cms will drop Qts to 0.35,
(0.5/root2), Fs decreases by / root2 and Vas increases by x root2.

However if Vbox is a lot less than Vas, usually is for a low Qts driver,
halving Cms and lowering Vas will make little difference to sealed or
vented boxes, and in the latter case may be worse, due to poorer
handling of frequencies below the vent frequency.

rgds, sreten.
 
diyAudio Moderator Emeritus
Joined 2001
i.e. for a driver with Qts of 0.5 halving Cms will drop Qts to 0.35,
(0.5/root2), Fs decreases by / root2 and Vas increases by x root2.

Sreten:

Good to see you again. Thank you for your input, that puts things into perspective. Only one thing, in your quote don't you mean doubling Cms will drop free-air Qts and Fs and increase Vas?

As I understand it, raising Cms means making the suspension softer.

Otherwise, thank you very much, this clears things up.
 
diyAudio Moderator Emeritus
Joined 2001
Aucosticraft: You are right, the changes we are talking about usually do occur during driver break in. I just wanted to make sure what those changes were.

Chris661, nandababaji: Thank you for your answers, I thought that when you change the spider stiffness more than one Thiele-Small value had to change, but I couldn't be sure, (minimal-very minimal-expertise with equations, lol).

nandababaji-when you changed your PA speakers suspension, did you measure Fs just before you changed it or did you go by the published specs and only measured after the surround change? Reason I ask is that, especially after being used, Thiele-Small specs tend to change.

An interesting things about nandababaji's change of surround type is that, mostly dealing with home speakers, I have come to regard the spider as the real stiffness of the suspension, the surround is usually so pliable it affects things little.

Clearly, in PA speakers the surrounds are usually so stiff that they do indeed affect the overall stiffness and small signal bass performance. PA and professional speakers don't have a surround/spider system, they have internal and external spiders. :)
 
diyAudio Moderator Emeritus
Joined 2001
Seems to me, many woofers (especially pro woofers) have excessively low compliance and corresponding low VAS and high Fs. Most likely they do this so you can dump more watts in the voice coil without exceeding mechanical excursion limits. But it reduces efficiency at bass frequencies, so you either need EQ to go deeper, or get limited bass depth.

I think it has something to do with the fact that rock and roll brought in the amplified music wave, and the lowest note in normal tuning on a bass guitar is 42 Hz. Since the bands and DJ's have to lug these speakers around and amplifier power, (in the earlier days especially), was limited, it became a set of choices between cabinet size, efficiency and bass extension. Pretty quickly the standard PA or even bass box became 15 inch low or low-mid frequency driver, 3 cu ft internal volume, (more like 5 cu ft external volume), a 60 Hz F3 cutoff and sensitivities in the 97 or 98 range, sometimes stated as 100 db, lol.

That's just for a DJ or small band, larger bands with more lugging capacity have bigger boxes, bass bins and a bunch of other options which take up more space on stage and in transport.

Power is cheaper per watt now and theoretically you could make the same size boxes go lower with a lower sensitivity, but the problem is that while power handling has improved over the years, there are still limits about pumping power in the speaker before it dies. So they still like to keep sensitivity up, which means higher Fs unless you make the box larger.
 
nandababaji-when you changed your PA speakers suspension, did you measure Fs just before you changed it or did you go by the published specs and only measured after the surround change? Reason I ask is that, especially after being used, Thiele-Small specs tend to change.

An interesting things about nandababaji's change of surround type is that, mostly dealing with home speakers, I have come to regard the spider as the real stiffness of the suspension, the surround is usually so pliable it affects things little.


Hi, I measured Fs both before and after I fitted the foam surrounds, so I am satisfied about the change. I also expected much less change in Fs than I measured because the driver has a dual suspension (spider) fitted, so in this case the surround was contributing much more to the stiffness than I expected. Interestingly the drivers sound a bit more tuneful and articulate at lower volumes now, before I changed the surrounds I had to drive them harder to get any real bass and life out of them, as if the stiffer suspensions had more effect on small signal response. (Less than 1watt) Regards, Mark.
 
Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.