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a VERY GENERAL rule of thumb is this: A doubling of power will net a 3dB increase in output. This applies ONLY to a true infinite baffle loaded driver, and in an anechoic chamber. Boxed drivers, and automotive volumes all have a dramatic effect on the net efficiency, and maximum output of any driver in any given situation.

While it DOES require frequency, the others do not really come into play as much. You will have more output at resonance. Generally speaking, you simply take the Re (Reference efficiency) of the driver, and add 3 to that number for each doubling of power you will be applying to the driver.

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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."

So, there is no corelation between peak-to-peak excursion and SPL? I would think that a driver moving 2inchs peak-to-peak would put out a higher SPL then a driver of the same size/volume moving only 0.5 inch peak-to-peak.

Does anybody else have any info about my question? To me, it would seem feasable to get a really accurate equation for SPL based on a few factors.

Now as haemphyst said, resonance would screw up this calculation, but wouldn't it be semi-accurate else where in the frequency range?

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Yup, there is a corelation between excursion and spl, but it also has to do with the VC wireing, cone diameter, power requirements. All those fun factors. But one of the biggest is the actual vehicle your putting the subs into. 1 sub in a suv can hit 130 db, ,while that same sub, same box, , everything the same in a car could hit 120db, , , so its really impossible to get close.

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2003 Chevy Avalanche,Eclipse CD7000,Morel Elate 5,Adire Extremis,Alpine PDX-4.150, 15" TC-3000, 2 Alpine PDX-1.1000, 470Amp HO Alt.

I think there are two different discussions going on here. One, what haemphyst was talking about, is SPL for a given driver and amount of power, raw SPL, if you will. Haemphysts formula, minus some unknown variables, as he pointed out, is correct.

Two, is what poormanq started talking about, maximum SPL.

It is simply incorrect to assume that a 2" peak to peak subwoofer will be louder than a lower excursion subwoofer. As Alpine pointed out, there are MANY other variables that enter the calculation for both the lower excursion sub and the higher excursion sub. Also, at this point, it is foolish to consider the raw driver itself, outside of the practical application of an enclosure.

High excursion has an effect on power handling, which ultimately effects maximum SPL. Where one sub may reach its physical limits with 300w, a high excursion subwoofer might be able to handle 1200 watts. While this might sound great, remember that physics doesn't allow free lunches. In general that high excursion subwoofer is much less efficient and has less cone area because of its high excursion capability. So, the puny 300w low excursion subwoofer will probably be LOUDER from 0-300 watts than the high excursion subwoofer in similar qtc enclosures.

We've been having practical discussion about this in another thread. Like Alpine and Haemphyst said, there are a lot of unknown variables to any final in-car SPL determination. However, using some enclosure design software you can at least compare subwoofers against eachother. To my knowledge this sort of software modeling is the only way to obtain the most complete picture, outside of actually trying it.

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New Project: 2003 Pathfinder

You guys want to know the secret formula for SPL numbers?

YOU-$10.00+GUY WITH RTA=SPL measurement.

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Thans for the info kfr01, haemphyst, ans Alpine gy.

Ok, I understand that it is not possible to make a formula that works for different drivers in different enclosures, but is it possible to make a formula to calculate SPL based on excursion for single driver?

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Poormanq45 wrote:

Thans for the info kfr01, haemphyst, ans Alpine gy.

Ok, I understand that it is not possible to make a formula that works for different drivers in different enclosures, but is it possible to make a formula to calculate SPL based on excursion for single driver?

No.

Why are you so hung up on excursion? Excursion can HURT maximum SPL just as easily as it can help it. You need to look at the whole picture.

Also, what would be the point of a free-air, no enclosure, maximum SPL rating? Maximum SPL is LARGELY a function of the power fed to the subwoofer and the enclosure used. I see no point at all to your idea.

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New Project: 2003 Pathfinder

You're right, kfr01... I have NEVER seen even a reasonable efficiency on a high excursion driver. Those damn laws of physics again... Output is a function of RATE OF CHANGE, not how MUCH change (which is what excursion would effect)... Excursion is presently the biggest killer of output there is. BTW, I would consider 91-93dB a reasonable output on a driver with 2 inches of pk-pk. Good luck finding ANYTHING close to that. My 9122 by Eclipse is specified at 87, and that is probably a bit optomistic. The Ti 10 from Eclipse was specified at 84, but when my buddy at Harman spec'd it out on the Klippel machine, it actually settled on 78! 78dB/w/m!!! THAT IS ABYSMAL!!!!

I have a few posts regarding this issue under my belt...

Try this...

Or this...

Read some of those posts, and see if that'll answer any of your questions a little better...

I STILL think, though, that with all the technology we have today, why can't we have a low Fs, decent efficiency, long Xmax driver? With NdFeB getting so cheap, why we can't stack about 10 pounds on a motor, and boost that efficiency... Steven?

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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."

doesnt the reference efficiency in effect sum up most of the other variables of the sub such as xmax, cone surface area, size of magnet. etc?!

then there are other variables such as enclosure, vehicle, speaker placement, etc that will play into db drag scores.

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MECP certified, 5yrs experience, you probably otta listen bitch!!

NO!!! The efficiency of a driver is a stand-alone specification. All of those items listed CAN have an effect on the Re of a driver, but the driver's Re will be a spec of it's own. If I plug in all of the other T/S parameters for a driver, my JBL Speakershop cannot give me the Re of a driver (Actually, I never tried it... I'll give it a shot... It does, but it is based on the Qts, a combination parameter). If those were the items that "made up" efficiency of a driver, then how do you explain a one inch tweeter with a 100dB efficiency, and an excursion of .01mm and 10 watts power handling, but an 18 inch driver with 3 inches of excursion, and 2000 watts power handling only gets 87-90dB. Shouldn't the 18 inch driver with 3 inches of throw be WAY louder than the tweeter? (with one watt input - lets compare apples to apples) Here is the physics coming into play again... SPL is based on RATE OF CHANGE! A tweeter can move back and forth FAR faster than a woofer - and while the wavelengths are MUCH smaller from the tweeter, the speed with which a driver can change direction DIRECTLY affects the rate of change (between rarifaction and pressurization), therefore it's output capability at a given power level.

I know, somebody is gonna say "But we're talking about woofers, not tweeters." A driver is a driver is a driver... if I had a tweeter with 6mm of Xmax, it will be FAR LESS EFFICIENT than the above mentioned tweeter. The laws of physics do not change, just because the frequency band being reproduced does. Consider uthink's beloved Nakamichi component set - OK fine, it has GREAT output, at the expense of extension, and he himself admits that the bass response could be better. Me, I am running Morel MW-162s in my doors (which personally I feel knock the Naks d**k in the dirt), but I have to drive my 6 inch drivers with 370 watts per channel. Oh well, I am happy to do so, because I can go all the way to 50Hz (and with SPECTACULAR authority, I might add) with them. I am willing to trade efficiency for extension.

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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."

dedlyjedly, incorrect. Reference efficiency is a very valuable parameter. Alone, however, it really tells us very little about the driver's potential performance.

xmax is not used to calculate reference efficiency.

SPL is derived from the physical parameters Mms and BL.
Mms is the driver's moving mass.
BL is the motor force.

Neither of these parameters carry any direct relationship to xmax.

Reference efficiency can be calculated other ways - none of which involve xmax.

Reference efficiency does not tell us anything about total potential SPL in any way. (thermal power handling, xmax, etc.)

Edit: Damn, haemphyst beat me to the punch, well, our posts didn't completely overlap, so I'll leave this as is. :-)

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New Project: 2003 Pathfinder

Well, the reason I am thinking that Excursion has alot to do with SPL is that the Driver is basically like a piston. Think about the engine in your car. As the piston moves up in the cylinder, more pressure is created.

Try this. Put a subwoofer in an enclosure specifically designed for it. Wire everything up. And then create an enclosure to seal off the front of the driver from getting an "unlimited" supply of air to move. Put a Digital Water Column tester in both the front and back enclosure. Find some way to measure the excursion of the driver while it's playing. Feed the driver a signal. Now, only measure the Excursion and the pressure reading of the Water Column. If you exclude the measurement of power that you are feeding the driver, you should be able to find a correlation between SPL and Excursion.

I understand that high excursions cause inefficiency. But there must be some way to calculate the SPL of a driver. And the basic 3Db increase = Doubling power as you guys know simply does not work.

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Dood, as I have stated several times, SPL is RATE OF CHANGE! It matters not one WHIT about how much pressure a piston can produce in either the positive or negative waveform, (which is what your water column is measuring) but HOW FAST CAN IT GO FROM ABSOLUTE MAXIMUM TO ABSOLUTE MINIMUM... Otherwise seemingly identical drivers can have different efficiencies, based on MMS, Le, Bl. If any one of these changes, it WILL affect the overall output from a driver, but Xmax WILL NOT AFFECT IT!

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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."

Poormanq45 wrote:

If you exclude the measurement of power that you are feeding the driver, you should be able to find a correlation between SPL and Excursion. I understand that high excursions cause inefficiency. But there must be some way to calculate the SPL of a driver. And the basic 3Db increase = Doubling power as you guys know simply does not work.

Haemphyst, I totally agree with what you're saying, but I did some thinking and our friend here must be talking about how xmax LIMITS spl at a given frequency. Here xmax is useful, I think.

displacement (vd) = xmax * effective piston area (sd)
The more air you can displace the louder you can go - the piston hypo. Since piston area is fixed, a limiting factor of displacement, and thus SPL, is xmax. So, given an unlimited amount of power, effectively throwing out any considerations of efficiency, and forgetting about thermal limitations, xmax would be useful in determining xmax limited SPL. Once I realized what our friend poormanq might be getting at I searched a bit....

I found this spreadsheet you might find helpful. The famous Mr. Linkwitz hosts this: https://www.linkwitzlab.com/spl_max1.xls Part A is titled, "Excursion limited rms sound pressure level (SPL) for a driver in a closed box."

In other words, this calculates MAX SPL for a GIVEN FREQUENCY.

You can view the formulas on the spreadsheet, or just use it to do the work for you.

Anyway, thanks for pressing this issue. I found Mr. Linkwitz's sheet fascinating. Poormanq, have you downloaded WinISDpro yet? It does some of this for you too. I think you may enjoy playing around with it.

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New Project: 2003 Pathfinder

I'm curious to hear what Steven has to say about this, if anything.

(ppssst... when are my Extremis drivers going to arrive? ;-)

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New Project: 2003 Pathfinder

Thank you kfr01. I realize now that I was very unclear in what I was asking. It's amazing that you were actually able to figure out what I was asking.

Thanks for the link.

[quote]Dood, as I have stated several times, SPL is RATE OF CHANGE![/quote]
Isn't the rate of change called the Transient Response?

SPL = Sound Pressure Level.

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Poormanq45 wrote:

Thank you kfr01. I realize now that I was very unclear in what I was asking. It's amazing that you were actually able to figure out what I was asking.

Thanks for the link.

[quote]Dood, as I have stated several times, SPL is RATE OF CHANGE!

Isn't the rate of change called the Transient Response?

SPL = Sound Pressure Level.[/QUOTE]

No problem. However, Haemphyst was still right, "Sound Pressure Level" still is all about the rate of change. At full excursion, if moving too slow, pressure drops off. It just becomes a giant motor moving in and out. Excursion of the woofer just sets the LIMIT on how FAR the driver can move while it is moving.

This is very important to understand when comparing speakers!!! As long as BOTH speakers are being driven within their excursion limits, excursion becomes a NON ISSUE. i.e. If I have two subwoofers, one that reaches xmax at 1600w at 40hz with a 30mm xmax. The other has 20mm of xmax, still a great deal, and reaches that with 600w at 40hz.

If you "only" have 500 watts of power to those speakers, EXCURSION WON'T EFFECT SPL ONE TINY BIT. RATE OF CHANGE WILL.

This is where the EFFICIENCY of the driver is so important. With 500w, the lower excursion, probably more efficient, driver will have MORE SPL, even though the potential xmax is less.

Anyway, have you downloaded WinISD yet?

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New Project: 2003 Pathfinder

Yeah I downloaded WinISD Pro.

So, why do companies like Adire Audio have such "large" excursions on their subs? 22mm each way IIRC.

So what's the point of designing the sub, surround, and motor to be able to have that large of an excursion if it is known that the greater the excursion, the lower the efficiency? Why don't all companies strive to increase the efficieny of their drivers instead of designing them to have large excursions?

Is it just a marketing gimmick to appeal to the uninformed american public? I mean, it's the American mentality that more is Always better then less posted_image

. I was talking to a guy in the local Car audio shop today about the Adire Shive and Bramha that they had. He kept mentioning the excursion. I guess he sells more speakers if he says a "high" excursion number posted_image

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2 reasons for excursion:

1) You hit the nail on the head. Excursion is sexy.

2) Maximum SPL can be much higher, because the driver has the potential to displace more air, and driver box size can be smaller. This makes high excursion ideal for car audio. Remember that displacement = cone area * xmax. If xmax is low you must have a much larger cone area to displace the same amount of air.

Take the Brahma, it can operate in a TINY! box. Which is awesome for car audio use. It's max SPL is LARGE. Like I said, however, there are no free lunches. In exchange for these positives you lose efficiency.

Thus, there is no "perfect driver," high excursion is right for some people/applications and wrong for others.

What do you think of WinISD, have you played with it, comparing different drivers?

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New Project: 2003 Pathfinder

Yeah, WinISD is a neat program. I have been comparing a few of the "big name" subs.

Well, I still am wondering. Why don't the companies focus on increasing efficiency instead of increase excursion? I mean, why not try to develope a sub with an efficieny of over 100Db 1w/1m @2.83v, and can handle 300~500w RMS? That would be a loud sub. And if the excursion was kept low, let's say less then 0.75in peak-to-peak, it would be extremely easy to prevent side to side motion from occuring.

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Poormanq45 wrote:

Yeah, WinISD is a neat program. I have been comparing a few of the "big name" subs.

Well, I still am wondering. Why don't the companies focus on increasing efficiency instead of increase excursion? I mean, why not try to develope a sub with an efficieny of over 100Db 1w/1m @2.83v, and can handle 300~500w RMS? That would be a loud sub. And if the excursion was kept low, let's say less then 0.75in peak-to-peak, it would be extremely easy to prevent side to side motion from occuring.

Well, because of the same reasons I stated earlier. Massive excursion allows the woofer to produce greater displacement with smaller drivers in smaller enclosures. This is very valuable in cars, as space is at a premium. But you're right... Pro audio generally uses higher efficiency lower excursion woofers. Stevdart and I actually had a conversation about this recently. I think we were comparing 2 generic but very efficienct 12" pro sound woofers to one Brahma. Basically for SPL above 40hz or so the 2 12" pro sound woofers kick the snot out of a single Brahma. However, they require a 5ft^3 ++ box to operate like this. The Brahma would work great in a 0.5ft^3 box. Also, the Brahma had better low frequency extension even though it had smaller cone area, because of its excursion capability.

There is a high efficiency following in home audio. Basically most tube amplifiers you see are very low wattage and are meant to drive high efficiency speakers. Adire makes a bookshelf speaker that is high efficiency, works well with as little as 3 watts and is 95db sensitive.

With amplifier power being cheap and true home audiophile grade stuff just being impractical for car audio use, I don't see high efficiency catching on in car audio. However, that doesn't mean you can't be a smart consumer rather than fall prey to the "MORE IS BETTER EXCURSION RULES!" trend that seems to be going on. I see real value to high excursion for SPL people. For daily drivers, SQ cars, and just about everyone else not willing to spend big amplifier dollars, I think that the smartest strategy is to evaluate the space you need to operate in, your sound quality and level goals for the system, and the amplifier power willing to throw at the subwoofer... I'd take those considerations and use them, together with software modeling and education like we're conducting, now to make the smartest buying decision.

For me it was a lower excursion more efficient sub that operates within my goal levels at 200w. For others it will mean a RE XXX with 1500w in a low Q sealed box with a band of +3db of parametric eq around 30hz to really make the bottom end deep.... It'll change along w/ goals :-)

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New Project: 2003 Pathfinder

Poormanq45 wrote:

[quote]Dood, as I have stated several times, SPL is RATE OF CHANGE!

Isn't the rate of change called the Transient Response?

SPL = Sound Pressure Level.[/QUOTE]

No, transient response is a drivers bility to react, FROM A STATE OF REST, and be able to accurately follow the electrical curve, accurately reproducing acoustically the original signal. Poor transient response is indicated by smearing or inaccurately following the electrical impulse. SPL, or sound pressure level is determined by a driver's ability to go from out to in (WHILE ALREADY IN MOTION) in the minimum time. Transient response has LITTLE, IF ANYTHING to do with a drivers maximum output capabilities.

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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."

"sound pressure level is determined by a driver's ability to go from out to in (WHILE ALREADY IN MOTION) in the minimum time."

So, does that mean that a tweeter can produce a much higher SPL then a Sub? I mean, tweeters usually go up to, and above 20K Hz. That requires a really fast response time.

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Look what I found:
https://www.silcom.com/~aludwig/Physics/Exact_piston/Exact_piston.htm

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[QUOTE=Poormanq45]Look what I found:
https://www.silcom.com/~aludwig/Physics/Exact_piston/Exact_piston.htm[/QUOTE]

What exactly do you think you've found there?

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New Project: 2003 Pathfinder

Poormanq45 wrote:

"sound pressure level is determined by a driver's ability to go from out to in (WHILE ALREADY IN MOTION) in the minimum time."

So, does that mean that a tweeter can produce a much higher SPL then a Sub? I mean, tweeters usually go up to, and above 20K Hz. That requires a really fast response time.

Well, most tweeters ARE much more efficient than woofers. Thus, given the same amount of power, tweeters DO produce more SPL than a sub. This makes perfect sense. Remember our friends Mms (moving mass) and motor force (BL) that comprise SPL? Well, if the moving mass is very small the motor force doesn't need to be large to produce large SPL. The rate of change haemphyst was talking about can be extreme.

Your asking this question actually probes at the usefulness of xmax. Producing a 10khz tone through 1" tweeters you can hit ear piercing SPL levels if fed enough power. However, like haemphyst stated earlier, drivers are drivers, xmax limits tweeters too. The same tweeter probably won't be able to produce a 1khz tone at the same spl level without greatly exceeding xmax. It'll probably be damaged. Excursion limits maximum spl differently at different frequencies.

Again, xmax shouldn't be used to determine SPL, it should be used to determine max spl at a given frequency.

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New Project: 2003 Pathfinder

Sound Pressure in the Far-field

Using the definition of f o in the wave spectra section, equation (W19), the sound pressure in the far-field can be written
posted_image

So apart from minor changes in notation, this is identical to the exact boundary integral result. A rather remarkable consequence of equation (P6) is that for a constant value of u0, on the z-axis the pressure is a linear function of frequency from DC up. Considering the complex behavior that occurs as a function of frequency, this is extraordinary.

Sound Pressure in the Near-field

Substituting the solution for D(b ) into equation (P2), the pressure at an arbitrary point in space is
posted_image

This integral is tricky to evaluate numerically. To obtain results at the baffle surface z=0 it is best to divide the integration range into 3 segments. The first segment from 0 to 4k is evaluated using a change of variables b =sing . From 4k to 10k the form above works best. The final infinite segment can be evaluated as a Weber-Schefheitlin type integral [NBS Handbook equations 11.4.33 and 11.4.34] less another numerical integration. A plot of the pressure at the baffle surface z=0 shows the result of this equation as solid lines, for ka=2p [30kb]. The piston velocity profile is in blue. Pressure is normalized by Zo, so it is expected to approach the velocity value of 1.0 for large ka. The result of the boundary integral is shown by the dots. A rather dense set of integration points were used, spaced .01 wavelengths apart. The pressure was evaluated at z=.05 wavelengths, and then a phase shift applied to approximate the surface value. Finally, the results of the numerical solution are shown, as the dashed line. I am quite happy with the agreement between these three results. The boundary integral is off a bit, but the agreement between the other two is pretty darn good. In all of the remaining plots, the exact equation result is shown as a solid line, and the numerical result as dashed. The agreement so good you have to look carefully in some cases to see that there really are two curves.

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Right, that's what the page says, but what do you think this means with regards to our discussion?

To me it simply tells us that for some generic driver we can obtain numerically _relative_ pressure for a point in space, either in the near or far field.

In other words, I think this page helps us little. We're talking about finding either specific or maximum pressure based on physical parameters on a specific driver.

Someone correct me if I'm wrong, its been over a handful of years since I've had any reason to look at integral math.

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New Project: 2003 Pathfinder

Well, I thought that formula may apply to our discussion. I havn't yet equated it out yet.

Well, what is the best formula for calculating SPL right now? Is it still the basic 3Db increase requires 2x Power? Or is there a little bit more accurate formula out there?

I'm curious, do you think it is even possible to make a formula to calculate SPL for all drivers? I would assume that it must take into consideration alot of variables, including Enclosure size, Driver cone material, The resonance of the driver, and what else?

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"...I'm curious, do you think it is even possible to make a formula to calculate SPL for all drivers? I would assume that it must take into consideration alot of variables, including Enclosure size, Driver cone material, The resonance of the driver,..."
Uh, should we just flip back to page one at this point??

Correct you are, Stevdart. Poormanq, start again at page 1.

Remember the difference we pointed out between excursion limited maximum SPL for a given frequency... (the linkwitz sheet seems to be the best for this)

and SPL NOT LIMITED by excursion. If xmax isn't limiting the movement of the driver, it is a non-issue, and yes, you go back to the doubling of amplifier power = 3db rise.

Of course all of this is kinda moot with the help of modeling tools that do all the math for you for specific enclosures... So, learn to use a tool like WinISD for all your driver purchase decisions and you're good to go.

I think this topic is probably dead. Anyway, I won't be able to participate - I just got married on New Years Eve and will now be taking a week in Jamaica at an all-inclusive. Needless to say, I will not be posting to the board. ;-)

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New Project: 2003 Pathfinder

Hey kfr01, you and your wife have a good time in Jamaica! My wife and I did an all-inclusive there, stayed at the Wyndam Rose, and had the time of our lives. Red Stripe beer and Blue Mountain coffee, each some of the world's finest...not to mention other stuff I won't mention....;) Tip: take a suitcase of toilet paper and shampoo (the regular big bottles, not the hotel freebies...). BIG bargaining and purchasing power with those items on the local economy. Better even than US dollars.

So then, if WinISD is able to accurately "predict" the spl for drivers then there must be a formula for doing this.

I don't really like just imputing some numbers into a program and then having it "spit-out" an answer for me. I like know how the answer came to be. Does that make sense?

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The answers are derived from the OTHER parameters of the driver. THEY DONT GIVE A DAMN ABOUT THE EXCURSION CAPABILITIES OR NON-CAPABILITIES OF THE DRIVER! Forget Xmax - it does NOTHING for the formula... Just forget it!

Also, there is NO program that will accurately predict the maximum output of a driver, once that system ends up in a close boundary area - read: living room, theater, car trunk, etc. The results are derived from X driver with Y parameters in Z enclosure, true, but it is figured in a virtual reality anechoic chamber. YOU CAN'T GET THERE FROM HERE! Oh, and one more thing - FORGET XMAX - it does NOTHING for the formula!

BTW, have fun in Jamaica!

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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."

Ok, I've forgotten about maximum excursion.

So, if WinISD does not actually provide us with any information, then why do most of the "senior" members recommend it?

Also, [quote]"Also, there is NO program that will accurately predict the maximum output of a driver, once that system ends up in a close boundary area - read: living room, theater, car trunk, etc."[/quote]

So, by this statement you yourself are saying that there is a formula to calculate SPL for subs. And you yourself said that to do this your Must be able to completely control the environment of the sub.

So, lets assume that the drivers are in an anechoic chamber. Can a formula be developed then?

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Just to be helpful here, Poorman, because this thread has grown a few pages and hasn't satisfied your curiousity:

May I suggest you ask the authors of the WinISD program your questions relating to their equations at https://linearteam.proboards12.com/index.cgi

Another forum where you might find members who are interested in your subject might be https://www.diyaudio.com/

There are published sources as well, some of which are linked to on this site: https://www.the12volt.com/caraudio/caraudio.asp

Please keep in mind that this is a car audio forum and the general interest is in car audio gear and the situations that we all encounter with the installation of it. Good luck with your inquiries.

SPL formula?