# Is Xmax necessary?

Discussion in 'Speakers & Subwoofers' started by Matthew Will, Mar 11, 2004.

1. ### Matthew Will Stunt Coordinator

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Hello,
I recently asked a question about what really is the determiner for SPL when considering a subwoofer. I thought it would have to do mainly with the diameter of the subwoofer and the Xmax of the subwoofer. Something else I considered was Force = Mass X Acceleration. So would a heavier cone produce more force and, as long as its rigid enough, translate that force into moving more air efficiently. But it could also be considered that just a light but very rigid cone that tranfers energy efficiently might produce more SPL if the mass of the cone does not affect the SPL, just how far the cone moves and at what rate. One response however that I got from a forum member was this

" no. the port resonance(if applicable) and room gain (in the house) or cabin gain(in the car) are very important too. many of the loudest speakers in existance have quite small xmax."

So my question now, is XMAX necessary? If a sub was produced that had a 6" total XMAX would it be no louder than a subwoofer with a smaller xmax? I ask this with the condition that both subwoofers would be in their own correctly designed enclosures. Which would be louder if they played the same frequency, same room, etc. Do consider that it might take more power to move the one sub to 6". Matt

2. ### JamesDB Stunt Coordinator

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Maybe I can off a few thoughts in response. First your force equation is not what really matters here and really is too simplistic of an equation for real life. Actually you should be using the momentum along with vacuum, and gas viscosity equations. And then it should still be noted that a heavier cone will not pass along more wave energy necessarily because we are not dealing with solids but gas dynamics where energy dissipation occurs in much more complex ways. Another thing is that the momentum equations require a velocity factor. This means that assuming the cone is moving in and out at a certain frequency, it will take more energy from the amp to move a heavier cone at the same speed as the lighter ones. And given that fact that no energy transfer is completely without some kind of loss the baseball bat analogy comes in. If you hit the baseball with a bat of a certain weight there will be one weight that will tend to optimally transfer the energy though to the ball given all other factors such as player strength, air viscosity etc. A heavier bat will not necessarily drive the ball farther.

So when designing a transducer or cone, the question asked is how can we efficiently, without distortion create more air movement (waves with larger magnitude). Making the cone bigger is one way, increasing XMax is almost as good and may result in less distortion, creating more aerodynamic cones for higher frequencies may decrease friction and result in more accurate waves, but increasing the weight of the cone may not be optimal.

3. ### Brian Tatnall Stunt Coordinator

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I think that there are a few things that are confused here. I could type a lot, but let's start here.

Yes cone movement is necessary for any amount of sound to occur. However, Xmax is a defined type of cone movement and doesn't account for everything. It looks at the linear aspects of the driver, yet when doing SPL competitions in say car audio you are going to push the driver beyond Xmax and start hitting the mechanical limitations of the driver known as Xmech. So you need to define the question more. Are you looking for distortion fee spl or SPL for SPL's sake?

Xmech is the mechanical limitation of the driver.

Xmag is the magnetic limitations of the motor. Xmag is the Vd when Bl is 71% of its original value.

Xsus is the suspension limitations of the driver. Xsus is where the compliance of the suspension has decreased to 25% of its original value.

Xmax is the shorter of any of the above.

SPL for SPL's sake cares less about the second and third option and pays attention to the Xmech and ability of the driver to hold together.

Adding lots of mass to a driver has other limitations also so why F = MA may look like a quick fix to getting SPL when implimenting more mass into driver becomes an entirely different beast. In addition you are playing a frequency, which means you're not applying force just for forces sake.

Also drivers have different ways that they willl peak in different enclosures.

Honestly, there are a ton of factors when considering which driver will be louder. Xmax is just one of them and can give a good idea of how accurate the driver will remain as power and Vd are increased.

4. ### Brian Tatnall Stunt Coordinator

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The correctly design enclosure thing is kind of a misleading thing also. In a different room, or car a speaker is going to respond differently. For example one speaker might be louder in one room 'winning' and less loud in another since the room acoustics peak at the same place the driver peaks. Things like that aren't going to give you one box that is the best.

Might want to throw this over to the DIY guys...they care a lot more about all those parameters and stuff.

5. ### Matthew Will Stunt Coordinator

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I guess my questions were a little misleading. I was rushing out the door so I couldn't compose my thoughts as I wanted. Let me try again.

I am creating a hypothetical experiement for you guys to hypothetically answer. Here are the conditions

1. Both subwoofers are being used in the same room in the same sweet spot.
2. Both subwoofers are in different enclosures that are designed to work efficiently with their respective subwoofer.
3. One of the subwoofers has an total Xmax of 6" while the other has only 3" total.
4. Each subwoofer are driven by their own different amp that has the capability to push both to their limits of xmax without distortion. (I know this kind of cheats because the 6" Xmax subwoofer will have more power but that is what happens. I could give both subs the same amp to push to the 6" limit but it would blow the 3" Xmax sub.
5. Each sub plays the same frequency
6. Each sub is the same diameter.

So which one is louder? Does the larger xmax ultimately win in the spl department? If I'm still not asking the question correctly feel free to yell at me. Matt

6. ### Michael R Price Screenwriter

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Air displacement capability (Xmax times Sd) is most important at low frequencies because the amount of displacement required to produce a given SPL increases 12db/oct as frequency decreases. In other words it takes 4 times as much displacement to create 100db at 20Hz as it does to create 100db at 40Hz. So a speaker can be very very loud at higher frequencies without a high Xmax (example: 15" PA woofers playing down to 80Hz).

Matthew, a doubling of Xmax corresponds to twice the amplitude of the signal which is 6db. So the sub with twice the Xmax creates four times the acoustic power given unlimited amplifier power, etc.

7. ### ChrisWiggles Producer

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that would be 3db.

8. ### Chu Gai Lead Actor

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Well yes it is a defined type of cone movement that manufacturers specify but not according to some rigorously defined standard. It's up to the manufacturer whether they'll specify the Xmax as determined from the voice coil overhang, some specific non-linearity, or something else. This of course makes it difficult to compare one manufacturer's woofer with another. As is often the case, the Xmax is typically an optimistic value which doesn't account for any of the nonlinearities in either the driver or the suspension. All things being equal the driver with the greater Xmax will be capable of playing louder but just remember in the real world, all things aren't that equal.
Out of curiousity, what are you trying to get a handle on?

9. ### Michael R Price Screenwriter

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Chris, the acoustic power is related to the square of the amplitude just like amplifier power is related to the square of the voltage output. Therefore a doubling of *signal amplitude* is a 6db difference and a doubling of *average power* is a 3db difference.

I think Brian's above post is correct about everything. I would add that Xmax can be a "rough estimate" of the maximum excursion before obvious (>10%) distortion due to large signal nonlinearity. As I understand it, different drivers have different amounts of distortion below Xmax and distortion always rises quickly once Xmax (especially Xmag) is reached. And with some drivers the mechanical limits are not far beyond that.

10. ### Nathan Porteous Stunt Coordinator

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So whos gona hit the ball farther the guy with the heavyer bat or the lighter one

11. ### ChrisWiggles Producer

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Michael: help me understand. Wouldn't doubling the signal amplitude be the same as doubling the woofers, or doubling the power?

12. ### Matthew Will Stunt Coordinator

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I've been told that speakers themselves do not have distortion below their mechanical limits. Distortion is just a square wave when the amp tried to put out more signal than it actually can. More commonly called clipping. What kinds of distortion do speakers have below Xmax?

Last question right now. Is there a market for speakers with 6" total Xmax?

13. ### Edward J M Cinematographer

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A 3 dB increase will provide a doubling of the sound intensity, and a 1.414 increase in sound amplitude. And a 6 dB increase will provide a quadrupling of the sound intensity and a doubling of the sound amplitude.

All speaker generate distortion. It has nothing to do with the amp clipping. Harmonic distortion (the one we are usually most concerned with) occurs when harmonics (multiples) the fundamental signal are produced due to nonlinear behavior of the electrical, magnetic, or mechanical mechanism of the driver.

Some subwoofers generate far more total harmonic distortion (THD) than others, and we use THD at various frequencies and amplitudes as one of the most important benchmarks of subwoofer performance. A subwoofer with low THD at all frequencies and amplitudes within its normal operating range will sound clean and distinct.

Intermodulation distortion occurs when one frequency modulates another. High woofer cone excursion required by say a 30 Hz signal, will significantly modulate (for example) a 400 Hz signal. The 400Hz signal will increase slightly in frequency when the cone is moving forward, and decrease when the cone is moving rearward.

Generally, limiting the bandwidth of the driver or subwoofer is the best way to reduce IMD. This is one of the primary reasons 2-way tower speakers suddenly exhibit a marked increase in midrange clarity when they are high passed to a subwoofer; the mid/bass drivers in the tower are no longer being required to produce deeper bass and the more delicate 1000-2500 Hz frequencies at the same time.

Regards,

Ed

14. ### Chu Gai Lead Actor

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Ron Jeremy seems to think so.

15. ### Travis R. Agent

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What if an aluminum bat is used that was lighter then the wood bats?

16. ### Ryan Schnacke Supporting Actor

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So which is louder? The bat or the woofer? I'm thinking the bat's got a ton of Xmax ... but how many watts is it gonna take to really get that thing moving?

17. ### Michael R Price Screenwriter

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Chris, let's say you take two identical woofers and wire them in parallel. Assuming the amplifier is perfect, each woofer will do exactly the same thing it would do if it was the only one. That means the total amount of air displaced is doubled. But the acoustic power was increased by 6db, since the efficiency increased 3db due to the addition of the second speaker, and electric power was doubled (3db) due to the parallel connection. So a doubling of amplitude corresponds to 6db gain and a doubling of power corresponds to 3db.

18. ### Eric Eash Second Unit

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this is too broad of a question. X-max is necessary for loud, low bass. if the frequency you are trying to play is 15Hz, you better have a lot of Xmax. if you are trying to play 50Hz, X-max is not very important. also, different tuning will affect SPL and Xmax for different freqs. your best bet is to get a program like winISD, start picking drivers and modelling boxes, this will help you far better than what any of us can tell you.

eric

19. ### Matthew Will Stunt Coordinator

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How would a lot of Xmax not help for 50 Hz? As long as the sub keeps up and plays the correct note then it effectively creates more SPL right? Thats the whole concept behind the car audio competitions. All subs don't use the same Xmax at certain frequencies. I see no downside to a speaker with a huge xmax if low notes or extremely loud volumes are necessary. Matt

20. ### Brian Tatnall Stunt Coordinator

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Matthew,

Car audio SPL competitions are NO where near a matter of sheer Xmax. If that were the case everyone would be buying the same woofer.

SPL in competition is a combination of the transfer function of the car, in-car peak, peak of the driver, box peaking, ability to delivery power effecitvely at one time, structural integrity of the car, structural integrity of box, front wave to back wave combining, mic tricking, woofer to port to mic ratios, and a lot more.

Let me say it again SPL does not CARE about Xmax. They look more at Xmech and the ability of the driver to hold together time and time again after 3kw+ EACH.

With a LARGE burst of power you can push the driver forward BEYOND the Xmax of the driver to achieve greater displacement. The come coming backwards needs to be able t withstand smacking into its Xmech or have many spiders to keep it from doing so. Xmax only accounts for some of the cone displacement, but does not account for 'nonlinear' displacement.

If anything study Xmax more and you will learn that there is still cone movement OUTSIDE Xmax. In other words, Xmax is not the parameter that determines how far a speaker is able to move it's cone. Xmax is a defined type of movement, which is what I wrote about above.Therefore, Xmax is not what SPLer's look at solely when looking at a sub. For a novice yes it is an excellent indicator, but for high level SPL competition they look FAR more the whole picture. For example a speaker that 'prefers' sealed boxes and how no ability to peak with higher xmax, can be crushed by a speaker that 'prefers' a ported box with excellent ability to peak and lower xmax.

**yes there is THD, IMD, and an entire host of other problems within Xmax, but that for now is or should be the industry standard...some companies are always going to break the rules of the standard and publish their 2way Xmax when it should be 1way just like many amplifiers don't define RMS very well. That's just part of the audio 'game' right now**