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Acoustic suspension theory-- bass driver loading


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I want to make sure I am correct in my understanding of acoustic suspension theory as it relates to bass driver throw and the loading effect of the trapped air upon the movement of the cone.

Lets take two 8 inch drivers with long throw. The first one was designed to be used in a specific cabinet with a known volume of air inside and its throw was determined by the designer to be the best for that particular cabinet and volume of air. Its throw need not be much longer that the amount which can be used in that cabinet. Its in-room response (utilizing the benefit of room boundary reinforcment) reaches 40 hertz at the -3dB level referenced to 1K hertz at 10% distortion.

The second 8 inch driver was designed by the same engineer to operate in a much larger volume cabinet and it has a significantly longer throw than the first one. In its cabinet, it reaches lower frequencies than the first driver can in its own cabinet. It will play 28 hertz at -3dB with 10% distortion if located in the same position as the the first driver in its smaller cabinet. In the upper reaches, it is designed to respond so that it can cross over at the same frequency as the first, shorter throw driver, which is 140 hertz.

Now, we take the second driver and put it into the first, smaller, cabinet. Can it reach any lower than the first driver can due to its much longer throw, or is its throw not usable because of the volume of air inside the cabinet? My understanding is that it cannot play lower. Is that right?

Will the second, longer throw driver in the first, smaller cabinet reach the same 40 hertz at -3dB output as the first driver but at a lower distortion level than 10% due to its longer throw? I think that the answer to this one is yes. Am I right?

Are there any sonic disadvantages to using the second, longer throw driver in the smaller cabinet?

This is the jumping off point for any discussion that corrects my errors or adds the other variables and considerations which I have not included because I don't know what they are.

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I think you are comparing apples and oranges. The throw of a speaker is your terminology but I presume you are talking about the maximum excursion in millimeters the cone can travel before it reaches the extreme limit of its mechancical suspension. This is not directly related to frequency response as speakers can be designed to have extended low frequency response but have a limited "throw" or a long throw but limited low end response or both or neither.

Insofar as the "classic" analysis of acoustic suspension theory is concerned, I'm at a little bit of a quandry myself. The basic principle is to use the difference in pressure between air trapped inside a sealed box and the outside air to supply the restoring force to the speaker cone instead of the stiffer mechanical suspensions previously used, the reason being that this force is far more linear and allows response to extend much lower. I should really read Edgar Villchur's patent. As I understand it, he uses a theromdynamic analysis to explain his invention but I've got a lot of problems with that. Thermodynamics, the study of heat and energy transfer and conversion is usally applied to problems regarding engines, refrigerators, turbines, and their efficiency in performing work compared to an idealized machine which follows a "Carnot Cycle." This cycle consists of an adiabatic expansion where no heat flows, an isothermal expansion where heat flows across a constant temperature barrier, an adiabatic compression and an isothermal compression. I don't see how this analysis while not incorrect explains the most salient aspects of loudspeaker performance. Besides saying nothing about frequency response as far as I know, most energy pumped into a loudspeaker 95% to 99.5% gets turned into heat so it is by the standards of notoriously inefficient mechanical engines (about 70% inefficient) even more inefficient and the differences relatively negligable. Ironically, the better performing acoustic suspension designs are among the least efficient at converting electrical energy into mechanical energy.

The physical and mathematical model which I do find useful is Newtown's second law of motion as applied to forced oscillation. It exactly describes the motion of loudspeaker cones of all designs if you apply it properly and ironically uses the same equation as the electrical filter equation which describes the crossover network (except the letters used in the variables are different but it is exactly the same equation.) All of the cookbook speaker design formulae are derived from this law and are entirely consistant with it (to the degree they are accurate.) It has been well proven over hundreds of years yielding consistanly excellent correlation with experimental data. It says that three factors are related to the motion of the cone and frequency reponse of the speaker, the mass of the moving element, the spring constant which restrains it, and a velocity related component called damping. Adjust these three properly and you will get any frequency response you want. If you are given one variable as fixed, say the volume of the box, in principle you can get your desired results by adjusting the other two.

In practice, speakers are neither purely acoustic suspension or mechanically suspended but are a combination of the two. Even so, Newton's law still holds true but it has to be applied correctly. For instance, in ported enclosures, the restraining froce or spring constant is often a function of frequency. While early AR woofers were very loosely suspended, later ones became tighter indicating some mechanical suspension and Villchur himself said below a certain frequency all speakers could be analyzed as acoustic suspension.

By changing the size of the box, you are changing the percentage of compression of air a given cone excursion of a given size will make. This changes the restoring force. In general, the formuala predicts that all other things being equal, the smaller box will increase the resonant frequency and the Q (narrowness and height of the resonant peak) of a speaker. So in your example, putting the driver intended for lower extended bass intended for a larger box into the smaller box of the first driver you cited will cause an upper bass resonant peak and decrease the low bass output by causing it to begin falling off at a higher frequency. And this is exactly what some designers deliberately do to create the false impression of deep bass for inexperienced listeners especially in rapid fire A/B comparisons in dealer showrooms. There are ways to compensate for this. By increading the mass of the cone and the effectiveness of the damping material, the bass can be flattened and extended. The alternative is to use electrical equalization to compensate by tuning the frequency response of the signal path to a complimentary response curve. That's how the Bose 901 works in part. So these systems can be tuned mechanically or electrically or a combination of both to achieve any desired response curve within their power handling limitations and available electrical power.

I hope this helps explain it.

>I want to make sure I am correct in my understanding of

>acoustic suspension theory as it relates to bass driver throw

>and the loading effect of the trapped air upon the movement of

>the cone.

>

>Lets take two 8 inch drivers with long throw. The first one

>was designed to be used in a specific cabinet with a known

>volume of air inside and its throw was determined by the

>designer to be the best for that particular cabinet and volume

>of air. Its throw need not be much longer that the amount

>which can be used in that cabinet. Its in-room response

>(utilizing the benefit of room boundary reinforcment) reaches

>40 hertz at the -3dB level referenced to 1K hertz at 10%

>distortion.

>

>The second 8 inch driver was designed by the same engineer to

>operate in a much larger volume cabinet and it has a

>significantly longer throw than the first one. In its

>cabinet, it reaches lower frequencies than the first driver

>can in its own cabinet. It will play 28 hertz at -3dB with

>10% distortion if located in the same position as the the

>first driver in its smaller cabinet. In the upper reaches, it

>is designed to respond so that it can cross over at the same

>frequency as the first, shorter throw driver, which is 140

>hertz.

>

>Now, we take the second driver and put it into the first,

>smaller, cabinet. Can it reach any lower than the first

>driver can due to its much longer throw, or is its throw not

>usable because of the volume of air inside the cabinet? My

>understanding is that it cannot play lower. Is that right?

>

>Will the second, longer throw driver in the first, smaller

>cabinet reach the same 40 hertz at -3dB output as the first

>driver but at a lower distortion level than 10% due to its

>longer throw? I think that the answer to this one is yes. Am

>I right?

>

>Are there any sonic disadvantages to using the second, longer

>throw driver in the smaller cabinet?

>

>This is the jumping off point for any discussion that corrects

>my errors or adds the other variables and considerations which

>I have not included because I don't know what they are.

>

>

>

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Guest kaiser_soze

soundminded, you have an exceptional talent. You have taken something that is very complex and that nominally involves the study of differential equations, and have managed to extract the essential facts and describe them in a way that is understandable to people who lack either the capacity or the motivation to study those equations. My hat goes off to you.

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Soundminded, this is a good overview. Let me add a few comments:

- EV's acoustic suspension theory didn't reference thermodynamics, so far as I remember. Being at home now, I can't verify this with the actual papers, but I am pretty sure. The essence of the idea was that that relying on an air spring was a better idea than relying on a mechanical spring.

- Where thermodynamics came in was in his description of the use of stuffing material to increase the effective box volume. The claim is that some of the pressure of the trapped air could be exchanged back and forth with heat energy in a fibrous material. Technically, this is said to change the thermodynamics of the air from adiabatic to isothermal.

(Actually, this remains a slightly controversial subject. Clearly, there is some isothermal process that happens with the right kind of stuffing, but not as much as originally proposed. Simply adding damping to a SHO can lower its F0, and this seems to partly account for the early observations of the effects of box stuffing.)

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Dave,

Are you sure that the woofer used in the later Ensemble's is really the same? A stronger magnet or different coil might help adapt it to a smaller box, without much visible change.

More info is needed to make a valid assessment. I know an engineer who might know exactly what was used in these products, but he is out of the country for a few weeks. I'll check with him about this when we speak.

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Ken,

I have a recent answer via email from CSW on that very question, for that very reason. The answer is yes, they are the same, and this is the most authoritative one I can get for now. I told them that I can't see the inside of the voice coil so that is why I am asking.

Frankly, I don't know if there is anyone there who knows enough about the Kloss designs and their history to give a trustworthy answer. Maybe there is the knowledge or the design notes, I don't know. I do have a PSW II and the supposedly identical driver in my Chinese New Ensemble cabinets. I could take them apart and look at the backs of the speakers, but I just figured that even an identical physical appearance there would not be enough to answer the question, except for magnet size (and not even strength).

The person I need to ask is Henry, and he has retired to bask in the music of the spheres. Second best would be someone who was working with him when the driver in the PSW II was designed.

I was told by Walter Schofield, CSW marketing director for 9 years, that the PSW II driver is longer throw than the original. This was being designed at the time he was exiting the company. Knowing Henry's cost containing design philosophy, I wonder if the only functional changes were the longer throw and the heat sink for increased power handling. If everything else could remain the same, then he would only have had to put the driver into a larger box and use the box size and the amplifier equalization to extend the response to below 30 hertz. Do you think that this approach could have worked?

In this scenario, if I understand Carl's and your answers already given, this would mean that the modified driver would perform in the Ensemble cabinet just the same as the original one does. An elegant, Klosssian soultion. Oh, and change the basket construction to help make up the cost difference of adding the modifications.

Would rather be listening to records,

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It wasn't until about 16 or 17 years ago that it occurred to me that classic mechanics could be used to analyze the motion of speaker cones. Well I guess that's what you'd expect from someone who wasn't trained as a mechanical engineer or a physicist. An so I thought, humph, maybe I've looked at this problem in a new way. Then one day, I dusted off my Sam's Audio Engineering book and looked at it and saw that the real experts were way ahead of me.

I don't see the issue of the stuffing as controversial, I just don't agree with EV's view of it. I don't see how this infinitesmal amount of heat, far less than in generated by resistive heating of the voice coil or would be affected by changes in the ambient temperature and cannot be transferred back to mechanical energy in any meaningful way plays a thermodynamic role. As I see the role of the stuffing, it controls the velocity related frictional loss component "B" in the equation by forcing the speaker to work to push and pull air between the fibers, a kind of aerodynamic drag the speaker must work against. I found it interesting that assemblers of the Dynaco A25 reportedly adjusted the amount of stuffing in production of each unit by measuring the tuning of the system, probably the only way to accurately determine it for each woofer/box combination. Rather than increasing the effective enclosure volume, I think it actually decreases it, the space taken up by the fibers displacing air. Besides, if there were an advantage to having a larger enclosure, why not just build a larger enclosure?

I've considered experimenting by adding a small enclosure on the front side of the woofer with an opening effectively slot loading it but upon reflection, this would probably increase the spring constant of the system giving it another pressure barrier to overcome. I've also considered horn loading the front of one but havn't tried that either. The one way which can increase the effective enclosure volume is the isobarric design which puts a second woofer in the box effectively out of phase with the first. So when the primary woofer is increasing pressure by decreasing the volume of the box, the isobarric woofer is increasing the volume and visa versa. The problem there of course is that you eventually have to deal with the far side of the isobarric woofer cone which can work into a sealed space or a vented one and gets you right back to the original situation so I don't see what's to be gained.

I really owe it to myself to read the work of Thiel and Small. I'd like to see if or how they adress the problems of a tuned air column on which vented speakers ultimately depend in one way or another as I see it. As with any wind or reed instrument, it must have a sharply resonant frequency at which its resistance to air flow is negligable. An octave above it and with succeeding octaves, it also reaches a minimum. But at the midpoint frequencies between resonances, its resistance to air is greatest resulting in an freqeuncy response mechanical impedence loading curve which oscillates with diminishing amplitude as a function of frequency. I'd like to see how they get around that. You'd think someone would have marketed a design using multiple tuning ports possibly from multiple chambers with the same woofer or even multiple woofers tuned to different frequencies. Perhaps with two "reactive air columns" this is what Bose did with the 901 starting with series III. Anyone know? But from the point of view of devising a wideband woofer/enclosure system which can be tuned to have a relatively flat response, it seems to me that the acoustic suspension principle still offers the best possibilities.

>Soundminded, this is a good overview. Let me add a few

>comments:

>

>- EV's acoustic suspension theory didn't reference

>thermodynamics, so far as I remember. Being at home now, I

>can't verify this with the actual papers, but I am pretty

>sure. The essence of the idea was that that relying on an air

>spring was a better idea than relying on a mechanical spring.

>

>

>- Where thermodynamics came in was in his description of the

>use of stuffing material to increase the effective box volume.

> The claim is that some of the pressure of the trapped air

>could be exchanged back and forth with heat energy in a

>fibrous material. Technically, this is said to change the

>thermodynamics of the air from adiabatic to isothermal.

>

>(Actually, this remains a slightly controversial subject.

>Clearly, there is some isothermal process that happens with

>the right kind of stuffing, but not as much as originally

>proposed. Simply adding damping to a SHO can lower its F0,

>and this seems to partly account for the early observations of

>the effects of box stuffing.)

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In his book entitled "Advanced Speaker Systems", author Ray Alden devoted some ink to the subject of box stuffing materials and their effects that seems to support Soundminded's comments.

He says that in an unfilled enclosure, the driver changes the volume of air inside the box by compressing it, thus raising both the pressure and ever-so-slightly, the temperature of the enclosed air. This effect is called Adiabatic.

If fiberglass is stuffed inside the box it adds a large thermal mass which absorbs the generated heat. This is called an isothermal process. Since a mass has been added to the system the system's resonance is lowered. In practical terms dacron (polyester) can increase a boxes volume about 15% and fiberglass can increase it about 18%.

To learn more here are a couple of good references:

1) "The use of fibrous materials in loudspeaker enclosures" - JAES Apr. 1976 by L.j.S. Bradbury.

2) "The Thermo-Acoustic properties of Fibrous Matrerials", L.M. Chase, IEEE Transactions on Acoustics, Speech and signal Processing, August 1974.

Remember, it's all about the music

Carl

Carl's Custom Loudspeakers

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>Dave,

>

>Are you sure that the woofer used in the later Ensemble's is

>really the same? A stronger magnet or different coil might

>help adapt it to a smaller box, without much visible change.

>

>More info is needed to make a valid assessment. I know an

>engineer who might know exactly what was used in these

>products, but he is out of the country for a few weeks. I'll

>check with him about this when we speak.

>

Ken,

I forgot to express my gratitude for your offer of assistance. The Classic Speaker Pages community is fortunate to have your participation and that of other design professionals whose names may be less recognizable but whose comments are backed by qualifications and experience.

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I'm not sure I understand any of the logic behind this or the point it is trying to make. When a gas is compressed, it heats up. This is how a refrigerator and an air conditioner compressor works. It's called P*V work in the famous equation PV=mRT. When the gas is allowed to expand again, it becomes cooler. Were it not for the heat loss outside the conditioned space provided by the condenser, when the gas expands, it would return to the same temperature it started at. If the PV work generated much heat, the inside of the enclosure would have to get hotter until it reached equilibrium with the outside. Isothermal heat transfer is an impossibility because as what is called "the zeroth law of thermodynamics" says, heat flows from the hotter to the cooler. (You'd be amazed at how many hair brained energy saving schemes mechanical engineers come up with which eventually get blown out of the water because they forgot this simple fact.) There is no heat transfer in an adiabatic process, it literally means without heat flow. The concepts of isothermal and adiabatic expansions and compressions are theoretical ideals and that is why the efficiency of real engines is compared to a Carnot cycle where these mathematical abstractions are used. The heat generated by the resistive heating of the voice coil is far greater than could possibly be generated by P*V work. In an AR3 it is approximately 199 times as great (based on 1/2% efficiency. In the most efficient speakers it is no less than 19 times as great (based on 5% efficiency.) Increasing the moving mass could be accomplished by just making the cone heavier and not adding any stuffing. Were this done and the stuffing omitted, there would be no increase in damping due to aerodynamic drag and the speaker would have a very bad resonant peak.

I can understand that added mass, increased box volume, and added damping material all work to lower the resonant frequency but they are not equivalent changes to the system, even if they can be computed so that a certain change to fs of one is compared to a given change in another which changes fs by a comparable amount. Even so, the fact remains that the decrease in fs by the stuffing is offset to some degree by the displacement of air due to the physical space the fibers occupy. Therefore to optimize performance, both the type, amount, packing, and arrangement of the stuffing in the box is critical as well as the remaining volume of air space. I'll try to find the equation for another posting.

>In his book entitled "Advanced Speaker Systems",

>author Ray Alden devoted some ink to the subject of box

>stuffing materials and their effects that seems to support

>Soundminded's comments.

>He says that in an unfilled enclosure, the driver changes the

>volume of air inside the box by compressing it, thus raising

>both the pressure and ever-so-slightly, the temperature of the

>enclosed air. This effect is called Adiabatic.

>If fiberglass is stuffed inside the box it adds a large

>thermal mass which absorbs the generated heat. This is called

>an isothermal process. Since a mass has been added to the

>system the system's resonance is lowered. In practical terms

>dacron (polyester) can increase a boxes volume about 15% and

>fiberglass can increase it about 18%.

>To learn more here are a couple of good references:

>1) "The use of fibrous materials in loudspeaker

>enclosures" - JAES Apr. 1976 by L.j.S. Bradbury.

>2) "The Thermo-Acoustic properties of Fibrous

>Matrerials", L.M. Chase, IEEE Transactions on Acoustics,

>Speech and signal Processing, August 1974.

>

>Remember, it's all about the music

>

>Carl

>Carl's Custom Loudspeakers

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  • 3 weeks later...

OK, here's the equation for newtons's second law again as applied to forced oscillation which describes the motion of the cone;

Fcos(2pi*t) = m*a + b*v + k*x

Fcos(2pi*t) is the driving force as a function of time

m is the moving mass

a is the acceleration of the cone

b is the damping factor

v is the velocity of the cone

k is the spring constant

x is the displacement of the cone

In the actual application of this law, remember that each of the parameters m, b, and k can be a combination of several effects acting simultaneously. For example, the spring constant can be a combination of the springiness if the air trapped in the enclosure and the mechanical springiness of the suspension.

An approximate solution for the resonant frequency F(0) is;

F(0) = (1/2pi)* sq rt [(k/m) - (b/2m)*(b/2m)]

You can see by increasing the mass of the cone, the resonant frequency is lowered.

Adding or removing stuffing changes two parameters simultaneously. Adding stuffing generally increases b tending to lower the resonant frequency but it reduces the amount of air left in the box which tends to raise k and the resonant frequncy with it. Which is more important? That's impossible to say without knowing the details of a specific arrangement. For example, if the stuffing is packed so tightly that air cannot get between the fibers to increase aerodynamic frictional drag, the main effect is to merely reduce the air volume inside and increase F(0). If it is packed loosely, the increased drag may be the more important factor having the net effect of reducing F(0). This is why it is hard to exactly restore performance once you have changed the arrangement of, type of, or added or removed stuffing.

Remeber that critical damping factor is 0.707 which gives no rise in response as frequency is lowered. A lower damping factor gives a frequency response hump and is said to be underdamped. It is analagous to a car with bad shock absorbers hitting a bump and bouncing up and down. A higher damping factor results in a more rapid bass falloff and is said to be overdamped. It's analagous to the TV commercial where the pearl floats very slowly down inside a bottle of Prell Shampoo.

I've given some more thought to the thermodynamic arguement and I still don't see it as being useful for explaining the acoustic suspension phenomenon. It's not that thermodynamics don't apply, they always do, it's just that it doesn't tell us anything about the motion of the cone and any effect is so slight compared to direct resistive heating of the voice coil and variations in ambient temperature as to be negligable to the point of being overwhelmed by these other factors. Newton's second law of motion seems to me to be the best tool for this purpose.

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It occurred to me that there is an important difference between acoustic suspension speakers and other types which nobody usually mentions which may contribute to their lower harmonic distortion. While both types of woofers exert their driving force on the cone near the center, the restoring force of conventional woofers occurs at the center and at the perimeter edge while for an AS speaker it is spread uniformly over the surface of the cone. The AS cone has far less restoring force per unit area applied to it. To understand the implications of this, imagine holding a sheet of paper at its left and right edges. Moving it back and forth tends to flex the paper transversly to its direction of motion causing it to want to bend. Only the stiffness of the cone material resists this force. If the forces aren't exactly the same, the imabalance makes the tendency far worse. Now hold the paper between the palms of your hands. This is how an AS speaker applies restoring force to the cone. Moving the paper back and forth creates no tendency to flex. Perhaps this difference explains one reason for greater cone breakup and harmonic distortion in non AS woofers, all other things being equal.

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