Hi Karls-
Much of what you say I agree with. And to answer you, I need to qoute your statements below. However, there is a lot of peer-reviewed published research which disputes a couple of points you have taken as fact:
You say, "(1)The commonly bandied-about equation describing speed of sound changes based on stuffing density is patently wrong on its face, and almost no one seems to notice."
Yes, the EQUATION is probably wrong, but there are many research articles which have directly measured the dramatic DECREASE in the speed of sound with decreasing frequency. I have never seen an experiment that shows the opposite, I'm sorry. Some are in the AES Anthology reprints from Old Colony Sound Labs. I have studied them for many years and see no mistakes in the many methods used to make that measurement. I'd be interested in seeing any research that demonstrates the speed of sound does NOT change dramatically. But I can believe that a particular equation would be wrong.
"(2)There are all these theories about how the stuffing works, from the air causing movement in the stuffing to adiabatic/isothermal changes to who knows what else. From what I have seen, these are 90+% BS. Viscous damping due to air movement past the fibers is almost all you need to understand stuffing."
These theories differ, along with their perceived BS content, because we don't really know how the fibers behave under all types of signals- transient or continuous, loud or soft...
For example, fibers can couple as a unified mass at certain frequencies, depending on the type of fiber, its packing density, the orientation of its fibers, the length of each line segment, the loudness of the sound and its duration. If the fibers do lock together under certain signals, then quite simply there must be less frictional loss as the fibers cannot rub against each other (because they are locked together). And that means little attenuation. Furthermore, they would then behave as a mass/spring system on that signal- which means resonance. So, viscous damping is not all we need to know, as sound in fibers does not always encounter viscous damping.
As far as adiabatic/isothermal arguments- The pressure throughout the t-line (or any box) is subtantially constant. When it does change, it does not last long enough to initiate a temperature change. Those are two important numerical values to know, so one can use them to come up with a theory (and a decent equation) for why the speed of sound does indeed change- a theory and equation that fit the experimental data and fit all preceding theories and equations which other experimental data validated.
So, why is the pressure substantially constant at all points in the t-line or any box? As some air molecules collide with the fibers, that scrubs off some of their velocity with each impact- some kinetic energy is lost to frictional heat as the fibers are made to rub together.
Fiberglass is rough, microscopically.
Wool is lubricated by its lanolin, and also smoother. Experiments show that fiberglass absorbs some low bass and a fair amount of midbass, and that wool absorbs very little low bass and just a little midbass. So the connection to roughness/smoothness seems obvious. But the real kicker comes after calculating the actual pressure differentials (which are responsible for velocities) at any point in the line:
The speed of sound, even if lowered inside the line, is still really fast- if the woofer starts to compress that air at 50Hz (taking 1/200 second, 5 millseconds, to reach its max stroke), upon reaching that max 1/4" stroke, the initial sound pressure is already 4+ feet distant! That means the pressure EVERYWHERE in the line changes nearly instantaneously- there is no/little air flow! It also means the woofer cone is moving far slower than the speed of sound down at 50Hz, ~2.7mph down there (1/4" in 1/200th second).
And since (not IF) the pressure everywhere rises and falls at once, there is little pressure differential to be found across any one region, so any local velocities cannot be high- there's little molecular velocity to scrub off. Which is exactly why materials of all sorts fail to absorb anywhere near 100% in the lowest bass- the individual air molecules just aren't moving much, so there's little velocity to scrub off.
In fact, with the pressure high, the molecules are mostly colliding with each other, as they're orders of magnitude closer together than the distance between the fibers- experiencing far more lossless collisions with their neighbors than lossy ones with the fibers. With the pressure lower, they do travel at an average higher velocity before hitting their neighbors, which are still `way closer than the distance over to a fiber.
You say "[Viscous damping] is why the impedance curves come out so flat."
Yes, by supressing the upper resonance peak that the undamped line would normally generate, as explained in my previous post.
"In an undamped line, you have a whole series of sharp impedance peaks at n/4 for all odd n. (Note that these are pipe resonances just like in an organ, and that this is very different from a ported box, which has only two peaks which are compliance/mass resonances.) The stuffing removes these peaks entirely at even midbass frequencies,"
Well, not entirely removed, but otherwise I agree with you on most every point. Except that a ported box has three resonances- at the two peaks and at the minima between them. And so does a transmission line, but the upper one is usually pretty-well damped, and we still have both the impedance minima resonance and an ultra-low frequency resonance (record-warp range) which most tests don't bother to measure, so the impedance curve looks flat. But here, flat does not mean non-resonant.
"The stuffing... damps them extremely effectively at lower frequencies (including at the lowest 1/4 lambda resonance)."
I have never seen any experimental evidence of that at the lowest 1/4 wave resonance, unless the line is stuffed like a bell pepper.
"On the other hand, ported design is specifically intended to function without damping, for all practical purposes."
Yes. The trick is to have the damping "turn on" at the higher bass frequencies, so it doesn't sound like a box... and Phasecorrect, that is my answer to your first paragraph in your last post- that I found a way to keep the box really quiet above resonance, whether sealed or ported, after years of building t-lines and all other designs. The only energy storage is at resonance, an amount which comes with a critically-damped system. It is not a lot, nor is it "stored" for longer than a half-cycle of the LF resonance (= critically damped).
"In addition, although this isn't discussed much, T-line woofers have their fundamental resonance frequency dramatically reduced when placed in the line... the entire mass of the air in the line becomes coupled almost 1:1 to the cone... a very substantial increase in effective mass."
Yes on all points Karls, and that will also reduce efficiency. This coupled mass can disconnect though, but only at VERY soft SPLs and VERY high ones, for viscosity reasons beyond the scope of this thread, but in any fluid dynamics text.
"An argument could be made, however, that due to compressibility, the initial attack at higher frequencies is much faster than if an equivalent real mass were added."
Yes that argument could be made, as this would be the de-coupling I mentioned above, which does not happen at our "ordinary" SPL's. But if that "less mass" effect was indeed true at the woofer's higher frequencies, then all that would do is allow the same input voltage to come out LOUDER in the higher tone range below the crossover point- because there's less mass to push for the same voltage. But the rise time would not be any different- that was already limited by the crossover. Which means the woofer is not "faster".
"Speed" is determined by the woofer quality, and also how sloppy the designer was in allowing any fibers to come too close to its cone, as there is an invisible layer of air that remains attached to the cone several inches deep. If the fibers reach into that zone, they drag down the cone's velocity.
"Contrast this to a sealed box, where the only way to drive the resonance down is to add real mass,"
Not the only way. One could increase the woofer's compliance only, or increase compliance AND mass (plus change the box' size).
"[added mass] hurts the transient response at higher frequencies."
Intuitive, but wrong. Added mass hurts only efficiency, not the transient response (which is the same as high-frequency response). Transient response is determined/limited by the crossover point. This was in shown the AES Journals- clearly, nearly 70 years ago. Added mass would hurt the transient response (HF respopnse) if we were allowing that woofer to go up to say, 1kHz or higher. If the added mass is a high %, that would tilt the woofer's tone balance downwards from 100Hz on up, but that can be balanced back to "flat" by designing the woofer to have higher compliance (also clearly explained in the AES Journals). So considering the woofer is probably crossed over below 300Hz, then its rise time is not affected by additional mass, just its loudness and maybe the tone balance of the woofer on the way to the mid.
"And in addition, an argument could be made that decay at all frequencies occurs much faster as well, due to the high level of damping the stuffing provides."
That is a very good way of describing any quieter box. If quieter, then there's less energy returning to the cone, so the decay time on an impulse would indeed be less. But we cannot measure that directly- only indirectly, and by listening via before/after comparisons.
"This increase in effective mass at low frequencies is very nearly "something for nothing", and is probably why T-lines seem to have both "speed" and "weight".
It's not for nothing if you have to slave over a far more complicated and heavy cabinet- especially in production! However, t-lines sound like they have more "speed" because the designer probably picked a better, more linear-motored woofer that has a vented voice coil and spider, and also has kept the stuffing away from the cone's vicinity. "Speed" is also a result of a properly-built box, and t-lines are always strong cabinets. Sealed and ported boxes are usually weak, as their designers don't know woodworking well enough to make the strongest joints using less wood. And neither do their cabinetmakers, as they are not mechanical engineers.
The sensation of "weight" comes from the lower distortion of the better woofer and from the woofer stroking less at the impedance minima, and from extra low-bass output from the port. And from the port's LF time delay, as those delayed LF's also linger on longer, longer than the rest of the music- making them audible on their own. Which is not entirely amusical!
You wrote, "I cannot disagree about the [time] delay of the back wave [out the t-line port opening], but I question whether it is an audible effect at the very lowest frequencies (because, again, a properly stuffed line will absorb everything from the lower midbass on up).."
Karls, I don't understand your comparision here between 'lower midbass' and the 'very lowest frequencies', but...
"The question becomes whether an 8-ft delay is audible at 35 Hz. I can't say because I don't honestly know. It could well be."
It is, especially when you can compare it to a sealed system which goes that low without the t-line resonance. Remember- it is not just an 8' delay from the t-line output- the woofer has its own delay in getting moving, often equivalent to ~another 8' delay. So the t-line output is actually ~16' behind the midband.
"I am not trying to disparage the quality of a low-Q sealed box in any way, as I too think it is often the best real-world solution, but I think that there is a lot more going on in a "T-line" than is commonly appreciated, and worse, a lot of plain misinformation floating around."
You're right on all points. To learn more, refer to those AES papers, and others in overseas journals whose titles escape me, but for which I have copies on file if you want them- experiments done by experienced scientists who had nothing to gain from seeing the results come out one way or another- just performing basic research, then trying to come up with theories that fit that experimental data- which any theory must, or it is just conjecture.
Thanks for your thoughts, Karls- you make some very good points. It sounds like you have done a lot of reading and made many speakers.
Bigtee- thanks for your thoughts. You are right about what have just said about Vandersteen.
And Phasecorrect, you are generally right about everything in your last paragraph! With regards to the question in your first paragraph- I cross over high enough to the mid that the woofer has stopped changing phase due to its own mechanical/acoustic rolloff down at ~40Hz, and has not started changing phase due to its HF mechanical rolloff. I also figured out how to put an aperiodic damping on the back of our mids to keep their 70-100Hz impedance peak from "turning off" my simple first-order electrical crossover up at the 300-400Hz crossover points, and to keep its own LF phase shift from adding to the desired x-over phase shift. And all of that holds for what I did for our mids/tweeters at their 2.8-3khz crossover points. And then I minimized our cabinets (but not too much), separated the drivers so they reflect much less off each other, developed the cast marble recipe we use, and figured out how to make strong, yet slender woofer cabinets, as their walls are not 2-3" thick. Go hear them.
Too many speakers jam a crossover point onto the woofer just an octave or two above its LF resonance, so the unavoidable woofer mechanical/acoustic phase shift adds to that crossover's phase shift. Thus, nothing comes out right, and we also hear room positioning become critical. And to make up for their losses due to the phase cancellation between woofer and mid, we see those woofers measure `way too loud, which makes John Atkinson scratch his head, because "it doesn't sound like it measures!" Right. Because time is being left out of that measurement.
Please read carefully my previous post and look into the link I gave in it to understand more, because I don't know how much more I can explain about time coherence. The link I gave is much more about the mechanical limitations of the transducers- no reason to duplicate that here!
Mr. Bischoff, this is all your fault.
Signing off in the big snow,
Roy
Green Mountain Audio
