t/s specs and theoretical comparisons

This post is questioning my understand of some of the basics and T/S specs and how they theoretically apply to the comparison of how loud a sub can get. I'd appreciate thoughtful responses. I've never seen this information clearly discussed before in a manner which the general audiophile could understand, and that's what I'm looking for. Lets ignore any subjective thoughts or comments; Looking for pure theoretical facts right now.

These days, there are soooo many subs out there now, it's hard to know what to choose, and how to box them, and basic T/S parameters and what it means in relation to other specs could help a lot. Yes, there are shady companies falsifying their T/S specs, lets ignore that they exist right now.

Modeling subs of course is the best way, but there are some subs you can't get _complete_ T/S specs for, and there are so many subs out there that modeling them all properly takes forever. So if I can figure out what are the most important parameters to look at, I could eliminate some subs right away. But I've never seen anyone detail it in a simple relational comparison I'm looking for: Something that doesn't takes months of study to understand, but that gives a general idea of how the sub will perform in a given basic sealed or ported enclosure by simply comparing the most common T/S specs.

Here's what I've learned so far, please correct me if I'm wrong or even not quite right:
- The SPL rating of a sub tells how efficient at changing electrical power into sound.
- Xmax is the max 1-way travel, also called peak travel; peak to peak travel would be Xmax x 2
- Ohm ratings have to do only with how much load is on your amp, and hence how much power the amp puts to the sub, but nothing to do with how loud the sub can play with a specific power level.
- Wattage handling simply tells you how much power the sub can handle and has more to do with how long it will last than how loud it can get.
- Subs that move more air can produce more intense sound
- The farther a sub can throw, the more air it can move
- The larger diameter the sub, the more air it can move.

My conclusions thus far:
1) Based on what I know so far, if I had 3 subs with the same SPL, same power put to them, and the same size, they should play at pretty much the same sound levels. Right?

2) However if we increase power, each sub will increase until they reach their Xmax, and the one that reaches Xmax last will play loudest. Is this correct? Or am I missing some critical aspect?

3) To have the loudest sub in a specific enclosure, you want the one with the highest SPL, highest Xmax, and largest diameter.

Additional Questions:
a) How does using a sealed box vs. a ported box impact my conclusions?
b) What am I missing that's important?

Thanks for those more knowledgeable than me for sharing!

KyferEz wrote:

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- The SPL rating of a sub tells how efficient at changing electrical power into sound.

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1: No. The Eta null is the number you want to see when determining the actual efficiency. It will typically be less than 1%. The SPL rating or specification only tells you how loud that driver will play, when one watt of power is applied to the voice coil. It *can* be used as a basic guideline to determine how loud a woofer COULD play, at it's rated power... Each doubling of power (theoretically) adds 3dB of output. 85dB@1W 88dB@2W 91dB@4W 94dB@8W 97dB@16W et cetera...

KyferEz wrote:

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- Xmax is the max 1-way travel, also called peak travel; peak to peak travel would be Xmax x 2

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2: Yes.

KyferEz wrote:

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- Ohm ratings have to do only with how much load is on your amp, and hence how much power the amp puts to the sub, but nothing to do with how loud the sub can play with a specific power level.

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3: Mostly correct. The impedance of a driver will ffect how much power an amp can make. Amps don't put out power. They have power available for the driver or load to consume. A fine line, to be sure, but let's call it what it really is. If there is no load, the amp makes nothing, but the potential is always there.

KyferEz wrote:

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- Wattage handling simply tells you how much power the sub can handle and has more to do with how long it will last than how loud it can get.

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4: Again. Mostly correct. The wattage CAN give you an indication of about how loud a driver can play. A high efficiency, but "low" power handling driver could get louder than a high power low efficeincy woofer. See point 1.

KyferEz wrote:

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- Subs that move more air can produce more intense sound

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5: Incorrect. Long throw woofers will always trade peak output for extension. If you have a driver that's just a BEAST, and you can throw 1200 watts at it, it'll get loud, of course, but based on #4 and by extension #1, a short-throw woofer can certainly play FAR louder. There was a huge argument on this a few years back... I'll try to dig up the thread.

KyferEz wrote:

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- The farther a sub can throw, the more air it can move

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KyferEz wrote:

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- The larger diameter the sub, the more air it can move.

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6: Those are both true. That's simple mechanics.

KyferEz wrote:

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My conclusions thus far:
1) Based on what I know so far, if I had 3 subs with the same SPL, same power put to them, and the same size, they should play at pretty much the same sound levels. Right?

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Allowing for the three aspects, exactly as you put them, yes. Three different woofers, with equivalent efficiencies, radiating areas, and power applied, (AND IN IDENTICAL ALIGNMENTS!!! - that's important, too...) will all play roughly the same output.

KyferEz wrote:

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2) However if we increase power, each sub will increase until they reach their Xmax, and the one that reaches Xmax last will play loudest. Is this correct? Or am I missing some critical aspect?

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Not necessarily. The driver with the highest efficiency will probably play loudest, not the driver with the longest throw.

KyferEz wrote:

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3) To have the loudest sub in a specific enclosure, you want the one with the highest SPL, highest Xmax, and largest diameter.

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Nope. Highest efficiency. Throw the other specs away.

KyferEz wrote:

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Additional Questions:
a) How does using a sealed box vs. a ported box impact my conclusions?

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Dramatically. Vented enclosures will improve overall output for a given driver, but not all drivers will be optimally aligned in a vented enclosure.

KyferEz wrote:

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b) What am I missing that's important?

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Oh, so much more than can be addressed in this thread. You do seem to have a decent handle on the matter as of now, though.

KyferEz wrote:

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Thanks for those more knowledgeable than me for sharing!

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I hope I qualify. :)

Here's one of the links... The most important paragraph, relating directly to some of my responses above, is this one:

haemphyst wrote:

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Also, WOOFER EXCURSION HAS LITTLE TO NOTHING TO DO WITH THE ACTUAL OUTPUT OF A SYSTEM. Frequency response, yes, output, no... If this were the case, then Eclipse and Adire woofers (as we all know, two exceptionally long throw, and equally capable woofers) would be capable of WAY more output than, say, a Cerwin-Vega or JBL Pro... An equally powered Eclipse or Adire woofer will NEVER exceed the output of either of these drivers. You'll notice I chose two relatively short throw woofers to compare with. This is to illustrate the fact that shorter throw will almost always equate to more output for a given input power. Output is SPECIFICALLY determined by rate of change - how fast can the woofer change direction? This factor MOSTLY being affected by 1) voice coil inductance, and 2) magnetic field strength in the voice-coil gap.

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Not SPECIFICALLY what you asked for... But handy, nonetheless.

Still looking for more.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

T/S parameters (also called small signal parameters) tell you how the woofer is designed and built, but not always how it will perform in actual usage.  There are a lot of other factors to consider besides just the properties of the woofer, such as the properties of the enclosure and the way the system is installed.  These two have as much or even more influence on the final result that the woofer's T/S numbers.  Here's something I wrote a while back that might help:  https://www.the12volt.com/installbay/forum_posts.asp?tid=73962&PN=1

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I was looking for that thread, too... Couldn't find it! Thanks DYohn!

Additionally... Steven links to an Adire paper that is no longer available. I had the foresight to upload it to the12volt... :P

Here it is...

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Very good info, thanks. I'll read over everything in those links a few times.

The statement about the Xmax having little to do with a driver's output is confusing...

While I can understand that a woofer that changes direction faster can produce more SPL because it's compressing sound faster, and that a lighter, more compliant woofer is likely more efficient, I still find it difficult to understand how woofer excursion has "LITTLE TO NOTHING TO DO WITH THE ACTUAL OUTPUT OF A SYSTEM".

Why is this hard to understand? Because SPL is sound pressure level. Pressure is generated by speakers by moving air. So it would seem that being capable of moving more air would generate more pressure (SPL), right? Seems correct because if you play a 50Hz tone, as you increase volume, the woofer's excursion increases... So how can a woofer reach high spl when it's excursion is limited?

Of course if a woofer has an efficiency advantage it will obviously be louder with less power, but how can it contend with long-throw woofers when they can move, and therefore compress, more air?

I know I must be missing something critical...

Thanks!

Ah, I just re-read the paragraph in question. The statement is being made assuming equal power... So a long excursion woofer can exceed the SPL of one with a shorter throw, but will require more power.

But that still doesn't explain how a woofer with a short throw can acheive such high SPL. Is it simply because a woofer with a shorter throw can be lighter and more efficient and can change direction much faster?

KyferEz wrote:

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Ah, I just re-read the paragraph in question. The statement is being made assuming equal power... So a long excursion woofer can exceed the SPL of one with a shorter throw, but will require more power.

But that still doesn't explain how a woofer with a short throw can acheive such high SPL. Is it simply because a woofer with a shorter throw can be lighter and more efficient and can change direction much faster?

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Generally it's because shorter Xmax goes hand in hand with higher efficiency.  But it has nothing to do with the weight of the system.  Weight (and woofer size) has nothing whatever to do with woofer speed.  That is a function of voice coil inductance.

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[quote]Weight (and woofer size) has nothing whatever to do with woofer speed. That is a function of voice coil inductance.[/quote]I beg to differ about weight... Just thinking basic physics, objects have inertia, therefore an object with more weight (or I really mean mass) moving in one direction has more inertia than an object with less mass, and therefore the object with more mass cannot change direction as easily as an object with less mass. Therefore, as I see it, it would take more power to reverse the direction of the woofer travel, and thus a woofer with more mass is less efficient...

KyferEz wrote:

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I beg to differ about weight... Just thinking basic physics, objects have inertia, therefore an object with more weight (or I really mean mass) moving in one direction has more inertia than an object with less mass, and therefore the object with more mass cannot change direction as easily as an object with less mass. Therefore, as I see it, it would take more power to reverse the direction of the woofer travel, and thus a woofer with more mass is less efficient...

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That's a common misconception.  Here, rather than try to explain it myself read this paper.

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I agree with what that paper is pointing out, it makes sense. That said, there was one point glossed over that I want talk about some.

That paper points out that current is proportional to acceleration. Not equal, proportional. Acceleration "is
strictly a function of the current through the driver". To show the math:
a = i(Bl/m)
That function states that acceleration equals the current times the Bl divided by mass. Efficiency is not a time-dependent problem, so you cannot substitute C in place of the variables when using the formula. Therefore as mass increases, efficiency decreases because it takes more current to keep acceleration the same. which is what I thought in the beginning: Heavy woofers are less efficient.

The paper is focusing on "does mass affect speed" and therefore transient response, a time-dependent measure, so they can replace Bl and m with C in the paper, which helps show the proportionality, however, it leads you to believe that efficiency remains the same regardless of mass, which is, as far as I can tell, wrong.

No, efficiency is affected by the total mass of the system.  If I said anything differently I must have misunderstood you.

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SPL is determined by rate-of-change. What that literally means is this:

How fast a woofer can change direction, to make the atmospheric high-pressure to atmospheric low-pressure gradients happen as fast as possible. Short time-frame, large-scale pressure changes (in millibars) are what determines SPL. The faster the peak pressure (in positive millibars) changes to the trough pressure (in negative millibars), the greater the SPL.

The lower the inductance of the voice coil, the faster the rise time of the current THROUGH the voice coil, thus affecting the acceleration OF the voice coil. With this being said, you could now see that it should be possible to have a high efficiency, long-throw woofer (they are just EXCEPTIONALLY expensive to produce) but it has nothing to do specifically with the throw of the woofer, or the frequency being produced; i.e. a long-throw woofer DOES NOT MEAN a "loud" woofer.

(I hope that made sense... I will have to re-read (with potential edits) after the LARGE bottle of Blue Moon Grand Crü wears off...)

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Gotcha. So in theory, to achieve maximum SPL with lowest power requirements, you want the fastest, lightest, largest, longest throw woofer possible.

Fast so that it moves peak-to-peak quickly
Light so it is highly efficient and uses less power
Large and long throw so that the woofer generates higher peak and lower trough pressures.

New question: Why wouldn't all woofers have extremely low inductance since it's so advantageous? Cost?

Long throw ONLY APPLIES when looking for low-frequency extension! It does NOTHING in the overall scheme of SPL!

SPL competitions are one-note applications. 60Hz is EASY to make in abundance, which is exactly why you see so many RF and CV wins in the SPL arena. Those systems will NOT go deep.

To address the inductance, you either have to widen the voice coil (re-tooling), add a shorting ring to the pole piece (re-tooling AND additional materials), or reduce the number of turns in the coil (lower power handling). Either expense or claims go out the window for any of the above solutions.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

What I stated came directly from what you told me... Here's how I came to those conclusions:

I'm using your own words... "SPL is determined by rate-of-change. What that literally means is this: How fast a woofer can change direction, to make the atmospheric high-pressure to atmospheric low-pressure gradients happen as fast as possible."

Lets say that the low-peak-pressure=p1 and the high-peak-pressure=p2. Now lets say the low-peak happens at time=t0 and the high-peak happens at time=t1. Rate-of-change is how much pressure changes during the timeframe of t0 to t1. So in this case:
Rate-of-Change=(p2-p1)/(t1-t0)

Now, going from nothing but how you defined SPL, it appears that SPL will increase because the rate-of-change increases. Say we make the low-pressure lower and the high-pressure higher WHILE keeping the low-peak at t0 and the high-peak at t1. The top of the fraction in the formula would increase, thus the Rate-Of-Change increases, thus SPL increases.

If this is wrong, please explain why.

Perhaps I am wrong in using that phrase... The one regarding the "nothing to do with"... It DOES have something to do with it: It usuall impacts it negatively. Look into the Eta null numbers, that one represented by "n0". That number is the representative figure, indicating how much electrical power (in percentage) is converted to acoustic power. Less than 1% is typical, and WELL less than 1% is fairly common. You will start to notice that the drivers typically described as "Long Throw", i.e. Eclipse Ti, TCSounds, Rockford T1's... Their Eta null numbers will be very low, comparatively speaking. If you examine the numbers of drivers from JBL, Cerwin Vega, they'll be quite high in the range.

Now... Conversely, many long-throw woofers will have outrageous power handling capabilites. These capabilities are enhanced (or maybe provided) by their amazing motor structures - HUGE magnets and giant, (high-inductance...) multi-layer voice-coils, low Fs... These capabilities and structures directly affect one another. The giant moving mass DEMANDS monster power to get the output levels that people are willing to pay for. Short throw, light, high Fs cones, smaller, lower-inductance single layer voice coils seen in many "lesser" woofers provide better SPL per watt... I say "lesser", because that's how people see them today. They'll ask themselves: Is it a fat surround? Is it 1500WRMS power handling? Those questions have all been influenced by cheap, multi-kilowatt amplifiers that cost $300.00. Big power is cheap to make now. Big power SINKS (the woofer) becomes the norm, and certainly ANY woofer being driven by 1.5 horsepower will be loud, right? There's the confusion.

Short throw woofers are generally preferred for SPL, using reasonable power. They just are more efficient, as a GENERAL rule.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Exactly, then we are in agreement... I didn't say so in my post 2 posts ago but I did recognize that woofer efficiency was far more important than Xmax.

Basically what I meant is that if you have 2 woofers with everything identical except Xmax, then take the one with the larger Xmax because it could reach higher SPL... And of course in reality, that never happens, so we have to weigh the options, and what you are saying is that longer throw woofers loose a lot of efficiency, and there goes the SPL for a given power level.

KyferEz wrote:

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for a given power level.

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is the key.  If you are not power limited, the longer Xmax woofer will displace more air and therefor produce higher dbSPL.

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DYohn] wrote:

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KyferEz wrote:

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for a given power level.

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is the key.  If you are not power limited, the longer Xmax woofer will displace more air and therefor produce higher dbSPL.

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^^COULD^^ produce higher SPL. And if it does, it's most likely JUST because of the enhanced power input, and NOT because of the enhanced throw.

In the same alignment, a short-throw CV woofer will ALWAYS output more SPL than a long-throw Eclipse Ti in the same alignment, even though the CV might be rated 250 watts, and the Eclipse rated at 1000. Even if run at rated power, there is still no guarantee that the Eclipse will produce higher SPL than would the CV, and I'd even bet cash that with 1/4 the input power, the CV will spank hands DOWN the Eclipse. With 4 times the power, there SHOULD be a 6dB benefit to the Eclipse, right? If it's EQUAL in output, I'd be surprised.

This is what I am trying to say. Long throw, in no way, ensures output superiority. At lower frequencies, to be sure, there will be advantages, but broad spectrum output, the longer theow woofer is actually handicapped.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Ah well Dave you and I will have to disagree on that one.  For any two woofers of the same size diaphragm and similar power utilization efficiency, the one with the longer Xmax always has more dbSPL capability  More swept volume = more air pressure generated = more output.

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...but this is what I'm SAYin'...

You'll RARELY if ever see a long throw woofer with an n0 even close to a short throw woofer. If their n0 numbers are similar, then they CAN'T have huge differences in output, at the same input power levels.

To say such a thing infers that the power conversion curve isn't linear, and that a given woofer COULD have a better power conversion efficiency at high input power than it does at a low input power... Right?

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

While those things are possible that's not what I'm saying.  If woofer A converts 100 watts of input to 6mm of linear motion and woofer B converts 100 watts of input to 16mm of linear motion, which one will produce higher dbSPL?

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DYohn: It still could be woofer A. How, why? Because woofer B might be far slower. Remember, "SPL is determined by rate-of-change". So if woofer B had a lower rate-of-change because of being slow to transition from the low-pressure trough to the high-pressure peak, then woofer A would produce more SPL. Right haemphyst?

Here's another thought:
What does the n0 mean exactly? Yes, I know it's the efficiency of the woofer turning electrical energy to sound energy. But, what does it mean mechanically for the woofer? If I understand this all correctly, it means that when comparing two woofers, the woofer with the higher n0 either moves faster, farther, or some mixture of the two with a given power than a woofer with a lower n0.

Humm, basically all I did was repeat other conclusions... I'm seeing a common theme here :)

Now, what about the compliance of a woofer. If a woofer is more compliant and another, then that leads to the idea that a compliant woofer is more efficient because it takes less power to move it, right?

I've been away from my keyboard... :P

DYohn: At what frequency? If woofer B is converting the SAME 100 watts at a frequency that is a full octave below what woofer A's Fs is, then no; as you know that lower frequency demands the extension of the suspension. If you are putting them on an equal playing field, 100 watts, 100Hz, similar n0, and equivalent alignments, then yes, you are absolutely correct. I never denied that though. *My* issue is that there AREN'T any long-throw woofers, certainly not any woofer B's with three times the throw of woofer A's, AND with an equivalent n0. THAT'S what my stand is. *IF* all things are equal EXCEPT excursion, then yes, the long throw woofer SHOULD be able to produce a higher SPL. Such a woofer doesn't exist, though.

Consider this: If everything is equal as stated above, then why would woofer B EVER HAVE TO EXTEND like that? It simply wouldn't ever happen. For the same frequency, for the same Sd, for the same power, for the same alignment, for the same n0, the extension WOULD HAVE TO BE THE SAME, yes? All above the same, the SPL would be too... Am I right?

For additional extension, there would have to be either

a: lower frequency
b: more power
c: higher n0

I think I'd stand on those conclusions...

KyferEz, you are correct.

To your second conclusion: n0 could be said to be a mathematical representation of the strength of the motor. The stronger the motor, the higher the conversion percentage. That's the mechanical difference. A smaller magnet, fewer turns on the voice coil, smaller wire in the voice coil, a thick top-plate, heavier diaphragm, higher impedance... Those could all affect the strength of the motor, and directly affect the conversion capability, thus the SPL ability.

To your third conclusion: I honestly do not know... I've never really looked at that aspect of SPL. It does stand to reason that a softer compliance would react faster to a large-signal input. That one, I'll have to ask or research a bit. Good question!

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Perhaps we're talking at cross purposes here Dave.  According to Boyle's Law, the more displacement a piston creates the higher it will pressurize a space.  Since a woofer is a piston (and it is power that creates excursion, not frequency) the farther it is displaced the higher the pressure wave it can create.  higher air pressure = higher sound pressure.  I am not talking about efficiency or driver Q, merely physics of sound.

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I don't disagree with that... Not one bit. But what I *am* saying is that if:

Sd is the same
Power is the same
n0 is the same
Alignment is the same
Frequency is the same

Then excursion MUST be the same, as well... It has to be.

JUST because a driver CAN have a longer linear excursion, that in no way means it WILL, especially if the conversion efficiency and the power applied are the same, AND if the frequency being reproduced is ALSO the same. Those are your test requirements/parameters. I'm trying to understand your explanations while living inside that same box. What am I missing if this is not the case? At a lower frequency, I know the driver will take advantage of the longer throw, but it's for lower frequency efficiency than you can achieve with a driver built with a shorter throw. I understand completely that power creates SPL. I also understand that SPL is NOT just pressure. SPL is (as I've stated) rate of change. It's pressure DIFFERENCES, in a given time period. Without a strong motor (high n0) to take advantage of the current being created by the amplifier, then a given woofer CAN MOST CERTAINLY have a lower peak SPL even with substantially more power being applied to the voice coil. This is typically the long throw motor.

Am I wrong? If I am wrong, please tell me WHERE I am getting disconnected! :)

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Well of course.  If the motors are the same the performance is going to be very close and only affected by the Qms of the drivers.  So we were talking about two different things.  You said earlier that a woofer with a shorter throw would generate more SPL than one with a longer throw.  I said rubbish, meaning in general a long throw woofer is capable of generating greater SPL.  But of course I missed the assumption you were making that they would have the same power efficiency.  If they do, then equal power will generate equal displacement.  You're right.  BUT, what if the short throw woofer runs out of Xmax with your power input while the long throw woofer has 50% of its travel left to go?  Which one would you want then?  :)

Me, I say go for large Xmax and feed it the power it needs. 

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...and perhaps to "poke the bear" one more time...

Go for large Xmax, feed it the power it needs (not wants) and tune for really deep Fb. (Where it will work better...)

When feeding more power to a longer throw woofer, WITH SIMILAR n0, yes. Longer throw woofer, please. I still maintain that you'll never see a really long throw woofer with efficiencies like the short-throw PA woofers for example.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

No, the sensitivity of a short throw woofer will almost always be higher since there is less wire in the voice coil.  But you go ahead and build a sub system with the PA woofer of your choice with 98db sensitivity and I'll build mine with the long throw woofer of my choice with 89db sensitivity and we'll see who can hit the highest numbers on the Term Lab.  Assuming you can fit yours into your car.  There is a reason people do not build SPL vehicles using Peavy PA woofers. 

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Ok, time to throw sealed enclosure vs vented enclosures into the mix.

I have done some simulations before using WinISD... It's been a while, but my overall conclusion was that sealed boxes have better low-end response and sq but ported boxes could be tuned to peak hard at specific frequencies at a significant loss of sq or tuned for smooth responses at a loss to some of the lower frequencies.

IIRC, I seem to remember that when I simulated a ported box designed to have a smooth freq response, and a sealed box of about the same volume as the ported one, then the sealed box often had higher simulated output...

Thoughts?