Acoustic suspension principal

[ironlake]

Does the stuffing the of cabinets to control Q to the .5 actually change the electrical impedence or to mechanically control the woofer for a nearly flat response. If this question is out in left field do not feel bad to shoot me down the tubes as I am still trying to fully understand the acoustic suspension principal, especailly all the reading I have done on the rather hard to understand Q.

[Carlspeak]

Stuffing an AS box does change the impedence hump at box resonance. As stuffing qty is increased, the hump lowers and moves to the left as box resonance drops accordingly.

Incidentally, the box Q of 0.5 you mention is quite low and sometimes hard to achieve. Ideally, a Q of 0.7 or so provides optimum base extension without any boombox type of sound. Those who want boombox sound target Q around 1 or even higher. Try doing a search using stuffing as the search word. You'll find lots of threads here on the subject. Those written by johnieo are probably the best.

Below is an example of what happens to the impedance curve around the box resonance frequency. It was borrowed from a conprehensive analysis of box stuffing by johnieo.

[soundminded]

The acoustic suspension principle (and how other woofer/enclosure systems work as well) is easy to understand if you first study Newton's second law of motion as it relates to forced oscillation. This can be found in any first year college physics book. This law was discovered hundreds of years ago and has demonstrated excellent correlation between the theory and experimental data. (It doesn't break down until you get to about 90% of the speed of light so there's no problem here.)

The law explains the mechanical relationships between mass, friction, and springiness. It is stated precisely in the form of what is called a second order ordinary linear differential equation. Stated slightly more famililiarly as an algebraic equation rather than as an equation in calculus, the equations is;

f(t) = ma + bv + kx

f(t) is the force on the moving object as a function of time. m is the mass, a is the acceleration, b is the viscosity coefficient (related to damping), v is the velocity, k is the spring constant, and x is the displacement. An approximate solution for forced oscillation with damping is given.

F (resonant frequency ) = (1/2pi)*(square root [(k/m)+ (b/2m)**2])

Usually a graph is also presented showing frequency response for different values of b (same as Q) the damping coefficient. The system can be tuned by adjusting these three values to yield any frequency response you want. The practical problem for an acoustic suspension speaker is that linear response to lower and lower frequencies results in decreasing efficiency and hence the ability of the amplifier to deliver and the speaker to absorb more electrical power. The actual tuning of the design for acoustic suspension speakers is probably done experimentally by trial and error to determine the optimal enclosure size and quantity of damping material for the driver selected.

The stuffing plays a vital role in damping in the acoustic suspension design. As the cone moves back and forth it pushes and pulls air between the fibers. This frictional aerodynamic drag is what reduces the speaker's tendency to vibrate with damped oscillatioin on its own, just as a car with bad shock absorbers will bounce up and down several times whenever it hits a bump. In fact, to design and tune a car's suspension exactly the same equation is used. The restoring force k is proportional to the displacement because it is the result of compression and rarifaction of air, a nearly ideal gas. Ideal gas laws show that the pressure of a given quantity of gas (in our case the air trapped in the box) is inversely proportional to its volume. Hence the restoring force is entirely linear for this type of speaker at any frequency. In other systems, the corresponding parameters are not nearly so linear or frequency independent. Other systems rely on the internal mechanical resistance (springiness) and damping of the speaker's construction which is usually not even close to linear as a function of frequency. In fact it was horrible at low frequencies during the era when Villchur invented AS. Also very critical the resistance to movement of the cone depended to one degree or another to a tuned resonant column of air just like the pipe in a pipe organ or the air column in a wind instrument (except for infinite baffle designs which had to be very large.) At some frequencies air flows through the ported opening to the outside easly, in others only with great difficulty. This is why ported systems typically have very high Qs, their usable bass response limited to a very narrow range and very irregular. In the early days ported systems had such high Qs that they were nicknamed "Johnny One Note."

Another not so obvious advantage of the AS principle is that since the restoring force on the cone is equally distributed over its surface by air pressure there is no differential force across the surface of the cone either circumferentially or radially as in speakers using mechanical restoring force. This reduces the speaker cone's tendency to break up under high stress. By its very nature it will have lower harmonic distortion all other things being equal.

Another advantage of the AS principle is that falloff below system resonance for a critically damped system (Q=.707) is 12 db per octave. This is equalizable making it possible to obtain linear response below resonance, at least an octave lower within limits of available amplifier power and speaker power handling capacity. For ported systems their 24 db per octave falloff below the system resonant frequency makes that frequency effectively its lowest limit.

While all low frequency speaker systems can benefit from additional techniques including skillful use of servo feedback and equalization for room acoustics and variations in source material, experience over the last 50+ years shows that the AS principle remains the best choice for low frequency speaker design. Newton's second laws explains why it is likely to remain that way. The mechanical properties of the speaker/enclosure system will affect the electrical properties as well. The system should be measured with the driver installed to establish crossover design parameters.

If you don't understand exactly how this idea works, don't get too discouraged. Edgar Villchur who invented it didn't fully understand it himself. His thermodynamic model which while not incorrect does not explain its actual mode of operation. That doesn't matter, getting the right answer for the wrong reason, even for no reason does nothing to diminish the fact that it is the right answer.

[ironlake]

Thanks greatly for the super explanation. You guys hopefully are teachers as you do a great job of making things easy to understand. You answered my question perfectly. The system has its electrical impedance controled by the mechanical changes the stuffing does to the speaker cone.

Now, what did ar do to the the model 9 to get the lower usable hz to 28 hz vs the 3a,s 35hz, more ftuffing or double 12 inch woofers or something else.

[Pete B]

When Villchur described the acoustic suspension woofer system in

the Audio Engineering publication he suggest a system Q of one.

Henry Kloss in an interview also suggested that a system Q of one

was best.

Allison designed the Allison One with a system Q of 1.

I would not describe a system with a Qtc of one as a boom box.

A closed box speaker is essentially a second order high pass filter

in the bass and they follow the design equations and frequency

response curves with associated Qtc as widely described in the

literature. See Figure 4 in Small's paper:

http://www.readresea...x_article_2.pdf

More T&S papers:

http://www.readresearch.co.uk/articles.php

[ligs]

The bass quality probably has more to do with the woofer placement in the listening room than just Q. I had AR 9 which AR said to have Q of 0.5 and AR 2ax with Q of around 1. Depending where they were placed AR 9 could sound boomy (in a corner as in many audio show rooms) or lacking bass(away from the wall). The bass quality of AR 2ax could vary a lot, depending on the room placement.

[Steve F]

Agreed that room placement can and does influence things quite a bit, but I also agree w/ Pete B that a Q of 1 is not a "boombox." Roy said that that was his target for most of his designs. The 9 has so much bass energy anyway that the designers could easily afford to "throw a little away," to put it colloquially, with a Q of .5. The 9 was a remarkably well-conceived and well-executed total system design, from the bass section's "automatic transmission," to the Allison-effect woofer placement, to the (then industry-first) recognition of the importance of vertical mid-tweeter alignment, and the recognition of the effect of early baffle reflections on perceived near-field sound quality and imaging.

Some individuals can have disagreements with one or more of these design aims, and that's fine.

But as a scientific/engineering excercise, the identification of the specific problems to be solved and the success of the 9's design in solving them remains a singularly brilliant achievement in loudspeaker development.

The 9 solved the specific issues it set out to solve, tangibly, objectively, and provably. That is very impressive.

(Oh, it also sounds great. Minor detail.)

Steve F.

[soundminded]

The Thiel Small parameters are a cookbook recipe for applying Newton's second law of motion and classic filter theory. They've simplified it to make it user friendly but it is exactly the same principle. How could it not be so? If it weren't it would be wrong.

A Q of 0.707 is not a matter of preference, it is the scientific definition of critical damping based on the Newtonian equation. Whether you like that result or not, that's the definition. It gives the most extended bass response without any peak. The overall bass response of the speaker takes into account the electrical circuit as well. This can be modified through filter design usually in the crossover network and/or equalization which is just another electrical filter. Superimposed on that are room acoustics and program material. The driver's reverse emf and electrical damping by the amplifier adds another variable. Designing for a Q of .707 does not mean that's where you should stop to optimize bass performace from a sound system but it is a very good start. It makes more sense to me than to introduce the additional variable of having to contend with one more resonance, an unncessary one. By designing AR9 to have a Q of .5 instead of .707 a greater bass boost and therefore more electrical power to achieve flat output below resonance is required than had it been otherwise. The explanation of why this happened isn't clear but it may have had something to do with the fact that with 2 nominally 4 ohm drivers in parallel, the filter to keep the combination from going much below 4 ohms would have been far more complex had .707 been the goal. It is also true that when extending bass that low, system gain can be so great that turntable rumble, feedback, all kinds of low frequency disturbances on recordings not othewise heard can become a real problem. Two levels of low cut filtering have proven very useful to me for addressing it when it's necessary.

[Carlspeak]

Here is a chart I was looking for but couldn't find when I wrote my original response to the OP. I clipped it off another forum.

It clearly shows how the theory of how box Q affects response at resonance.

[Steve F]

Exactly, Carl.

1.0 is no more above the 0dB line than .707 is below the 0dB line (before they both start their rolloff). 1.0 will be a little "fuller" sounding, .707 a little "dryer" sounding, but both are about the same deviation from "perfectly accurate" as the other, at least in the frequency domain. No mystery why Roy aimed for 1.0--just as accurate, and a bit more subjectively 'full.' Good design goal, especially for the 8" and 10" systems.

As with virtually all things in audio, preferences vary and for legitimate reasons, in the ear of experienced, educated listeners.

Steve F.