# does xmax matter in ported boxes,



## William_White

Does xmax matter in ported boxes and what does power handling do in a sealed box, if 2 sub woofers had identical displacement and FR but one needed twice the power to reach it would one be louder?


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## Oliver

X-max is a function of frequency in this case.

Lower frequencies are longer.

Around tuning frequency, the sound comes from the rear of the cone via a port.( The speaker doesn't move as much ). see videos on youtube.

Are the 2 subs going to be powered by the same amp or different amps, one for each ?


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## Hanatsu

William_White said:


> Does xmax matter in ported boxes and what does power handling do in a sealed box, if 2 sub woofers had identical displacement and FR but one needed twice the power to reach it would one be louder?


It matters some for the frequencies above tuning frequencies (Fb). At Fb there's very little excursion and almost all sound comes from the port. A woofer made for sealed enclosures need more excursion in the lower frequencies (excursion increases four times for each octave drop, ie 40Hz --> 20 Hz = 4x excursion). Woofers made for sealed and ported enclosure are often constructed slightly different, the differences can be seen in the T/S parameters.

For IB/Sealed it's quite easy, Sd (cone area) and Xmax dictates the volume displacement. The more air you move, the louder it gets at a given frequency. Higher power requirements does not make a woofer louder than an other, by requirements I mean 'power required to reach Xmax". Efficiency is determined by the driver itself and the enclosure its put in.


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## Patrick Bateman

William_White said:


> Does xmax matter in ported boxes and what does power handling do in a sealed box, if 2 sub woofers had identical displacement and FR but one needed twice the power to reach it would one be louder?


Output is dictated by two things:

1) the area of the cone
2) the xmax of the motor

For the most part, that's it!

There's a common misconception that if you have a woofer with a sensitivity of 80dB, and a woofer with a sensitivity of 99dB, that the 99dB woofer will play louder.

But this is not the case, for the most part. It's basically displacement that rules over all. (In my hypothetical example, the two woofers will both require exactly the same displacement to achieve the same SPL at low frequency. The only difference is how they get there. A 3.75" woofer can play as loud as a 15" woofer if the 3.75" woofer has enough displacement to generate the SPL. The advantage of the 15" woofer is that the woofer cone doesn't have to move as far out of the gap to get there. (Since the 15 is about sixteen times the size of the 3.75" cone, it will require about 1/16th as much xmax to achieve the same SPL.) *But the displacement required is exactly the same.*

There are some variables that make this more complex, but these variables don't have much impact as you get closer and closer to the F3 of the design.

Here are some of those variables:

1) Directivity. If one driver radiates into a narrower beamwidth than another, the first driver will have higher SPL on axis. This is how horns and waveguides work. This is not a factor for subs unless you happen to have a subwoofer that's the size of a semi truck. (40hz is 28 feet long!)

2) Comb filtering. If you have an array of drivers, they'll combine constructively *and* destructively. This isn't a big factor for subs, unless your subwoofer array is the size of a house.



Does that help? Basically it comes down to cone area and xmax. Therefor the answer to your question is "yes"


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## William_White

So when winisd says that larger sealed boxes are less efficient it is wrong. Now what about ported boxes how does power effect them since excursion is low at FB. This question arose from the SSA Xcon and Zcon.


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## minbari

I understand what you are saying, but with a 15" with 25mm of xmax, you would need a 3.75" woofer with 400mm of xmax. some things are just not physically possible, lol.

but I agree with everything else 

to the OP,

if you have (2) 12" and they both have 20mm of xmax and one takes 1000 watts to get there and one takes 250 watts to get there. they would be identicle. As Patrick said, SPL is determined by cone area X xmax. doesnt really matter how you get to that xmax as long as you get there.
This, of course, discounts cabin gain and any box tuning that might effect it to some degree.


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## minbari

William_White said:


> So when winisd says that larger sealed boxes are less efficient it is wrong. Now what about ported boxes how does power effect them since excursion is low at FB. This question arose from the SSA Xcon and Zcon.


when does it say that? almost every model I have done with winISD, the larger the enclosure the lower the Fc and the less power it took to reach xmax.


in a ported box since excursion is at minimum at the tuning freq, it comes down to thermal handling. if you have a box tuned to 30 hz and played a 30 hz sine wave, it would barely move, but you would melt the coil from overheating.


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## William_White

It says it on the spl graph, on the excursion graph it shows that the larger box has higher excursion.


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## minbari

William_White said:


> It says it on the spl graph, on the excursion graph it shows that the larger box has higher excursion.


I would have to see it.  higher excursion, by definition, will have more output.


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## Serieus

William_White said:


> It says it on the spl graph, on the excursion graph it shows that the larger box has higher excursion.


that means it's more efficient, more excursion at the same power = more output


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## Patrick Bateman

minbari said:


> when does it say that? almost every model I have done with winISD, the larger the enclosure the lower the Fc and the less power it took to reach xmax.


Output is determined by displacement. (xmax multiplied by cone area.)
If you look at the graph of the large sealed box and the small sealed box, you'll notice that the excursion of the large sealed box is greater. So the large sealed box WILL have more output with the same power, but at the expense of greater excursion. Conversely, you can dump more power into the small sealed box and get to the same SPL level as the large sealed box.

In a nutshell - xmax is the determining factor for output IF the cone size is equal and power is sufficient to get there.




Here's another weird way of looking at it:

Let's say you have a 12" woofer in a 28 liter box. You play a 40hz signal. There are a number of things which will determine how loud that 40hz signal is going to play, but arguably the four big ones are these:

1) is the xmax of the woofer large enough to play the 40hz tone? (IE, can it physically move far enough to make the tone?)
2) The size of the cone acts like a multiplier. Bigger cone multiplies the volume of sound.
3) The air in the box acts like a spring attached to the cone. As the cone tries to 'push' into the box, the air pushes back.
4) The strength of the motor counteracts the force of the spring from item 3


To me, the thing that's interesting is that you can ratchet up the motor force to counteract the action of the 'air spring' in the box. Basically more motor force means the 'air spring' has less and less of an influence. (IE bigger motor equals smaller box.)

This is how isobaric loading works also.

This is also why horn loaded loudspeakers like woofers with huge motor force. Basically the big motor force 'smooths out' the peaks and dips because a large motor exerts a stronger force against the cone than a small motor.

Note that this doesn't mean that a big motor is always superior. That was something it took me a few years to wrap my brain around, the idea that there are lots of situations where a small motor is superior to a large motor. (For instance, if you have the space for a very large box, you're generally better off spending $200 on two mid-range woofers than $200 on one high end woofer. Because displacement is tough to beat, particularly if you have the space for a large enclosure.)


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## thehatedguy

Actually isobaric works because you are adding the masses of the cones to one larger mass...so you have 2x the mms but half the compliance. The other T/S parameters stay the same for a single driver.


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## jp88

thehatedguy said:


> Actually isobaric works because you are adding the masses of the cones to one larger mass...so you have 2x the mms but half the compliance. The other T/S parameters stay the same for a single driver.


Bl would also double


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## thehatedguy

Why would BL double?


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## benny

two motors working in tandem?


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## thehatedguy

I don't think it changes.

As far as I knew, sensitivity is lower, compliance is half, and mms is double...and that's all that changes over a single driver's parameters. Could be wrong though.


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## BuickGN

I think it's double the Bl and the reason I think that is when I was researching it one thing that stuck in my head is that it was claimed that this configuration is rarely needed anymore due to the higher Bl of newer subs.


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## Hanatsu

The L (coil length) in (BL) would effectively be doubled if the speakers are wired in series so BL doubles, right?


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## Patrick Bateman

thehatedguy said:


> I don't think it changes.
> 
> As far as I knew, sensitivity is lower, compliance is half, and mms is double...and that's all that changes over a single driver's parameters. Could be wrong though.


When you go isobaric it "looks" like BL goes up. But that's usually because people wire the driver in parallel when they go isobaric, and current is one of the factors in the equation of BL. And current goes UP when you wire in parallel.

Finite Element Method Magnetics: Analysis of a Woofer Motor

"The parameter BL is the gain between an applied current in the coil and a resulting force on the coil. The name "BL" refers directly to the formula for Lorentz force on a wire:

F = iL X B


where F is the force, i is the current in the wire, L is the length of the wire, and B is the magnetic field to which the wire is exposed. The "BL" parameter is notionally the average radial field to which the voice coil is exposed multiplied by the length of the wire in the voice coil."


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## William_White

now that its been established how Power and Xmax affect ported and sealed enclosures, how do they affect bandpass boxes?


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## subwoofery

Depending on your subwoofer, YES Xmax matter in ported enclosures. 
I remember plotting a Kicker L7 something and that particular woofer couldn't be tuned low unless I made the box really small or really big (don't remember) - you'd reach Xmax around 45Hz or 50Hz, way before the tuning freq of 30Hz  

Kelvin


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## minbari

subwoofery said:


> Depending on your subwoofer, YES Xmax matter in ported enclosures.
> I remember plotting a Kicker L7 something and that particular woofer couldn't be tuned low unless I made the box really small or really big (don't remember) - you'd reach Xmax around 45Hz or 50Hz, way before the tuning freq of 30Hz
> 
> Kelvin


But unless you are building an spl monster, that sub is terrible.
If you are building an spl system,, [email protected] 45hz, problem solved 

Sent from my motorola electrify using digital farts


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## William_White

William_White said:


> now that its been established how Power and Xmax affect ported and sealed enclosures, how do they affect bandpass boxes?


 anyone


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## subwoofery

minbari said:


> But unless you are building an spl monster, that sub is terrible.
> If you are building an spl system,, [email protected] 45hz, problem solved
> 
> Sent from my motorola electrify using digital farts


Yeah, that's what I told my friend when he asked me to model his sub (I think it was an 8") - couldn't tune the enclosure below about 38Hz I think 
He wanted to use what he had for an SQ system

Kelvin


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## Patrick Bateman

William_White said:


> now that its been established how Power and Xmax affect ported and sealed enclosures, how do they affect bandpass boxes?


Every single type of enclosure works the same way in this respect. (Geddes has argued that there's one exception - the acoustic lever - but I don't know enough about that enclosure type to speak about it.)

For every type of enclosure type, output at the low end of the box is dictated by bore and stroke. (aka cone area and xmax)

There's only two real exceptions to this rule:

1) If you can restrict the radiation, efficiency will start to go up. This is how horns and waveguides work. In a car, the cabin itself does this, because the wavelengths exceed the dimensions of the car itself. This is why SPL cars invest a lot of effort to keep the car itself from flexing.

2) Horns and ports stop the cone from moving at certain frequencies. For instance, in a ported box tuned to 30hz, *the cone is not moving.* So voice coil thermal limits become a big factor at that frequency.


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## William_White

So they work like the rear enclosure; Xmax is less crucial in a 6th order/ported as long it can reach the tuning frequency before exceeding it and power handling is less crucial in a 4th order/sealed as long as xmax is acheived without exceeding it. Am I understanding this right?


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## Hanatsu

William_White said:


> So they work like the rear enclosure; Xmax is less crucial in a 6th order/ported as long it can reach the tuning frequency before exceeding it and power handling is less crucial in a 4th order/sealed as long as xmax is acheived without exceeding it. Am I understanding this right?


6th order BP acts like a "dual vented enclosure". You will have 2 different tuning frequencies, excursion will be low at both frequencies. Group delay ain't pretty either, but they have the capability to get quite loud. Have fun building one, they are hard as crap to get right even if you model them


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## William_White

I don't plan on building a 6th order unless some one gives me an 8" driver and a challenge.


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## stryke23x

There are a few things that can be visualized a little better with pictures. First lets get a few basics down. Patrick has covered most of it but just wanted to clarify a little. Some things to understand. 

SPL is always equal to the amount of air being moved or displaced. The diameter of drivers, efficiency, etc plays no part in this, only the overall amount displaced. 

The more air displaced with the least amount of power is better. A woofer that can move X amount of air with 300W is far better than another woofer that requires 2000W to move that same amount of air. There seems to be some kind of misconception in the car audio world that it is better to have a woofer that can "handle" tons of power than one that moves the same amount of air with far less power. The less power to get a given SPL the better the results. This keeps thermal failure and thermal distortions lower. Keeping less current in the VC also lowers the effects of eddy currents in the motor and as a result lowers distortion. The only benefit to a crazy inefficient woofer that can take tons of power is the ability for it to help heat your car in the winter. A 2000W electric heater can help warm up a vehicle quite quickly.

Every time you drop one octave, it takes 4x as much displacement to get the same SPL level. As an example 40hz takes 4x as much displacement to get the same SPL as at 80hz. 

Power handling of a woofer has nothing to do with excursion. Power handling is a thermal rating based on the amount of power the VC can safely take. It is very possible that you can damage a driver due to over excursion with far less than the rated power of the driver. The amount of power required to get to excursion limits is determined by the enclosure. People can build multiple size and enclosure types. As a result, a manufacture will never have a way to rate the amount of power a woofer requires to reach it's physical limits. This is something the installer needs to be aware of and pay attention to.

In a sealed enclosure only the front wave of the woofer is being used. The back wave is contained and not used. All displacement comes from this front wave of the woofer only.

In a vented enclosure, the back wave of the woofer is being used to sum with the front wave through the use of a port. As a result the woofer and port have an effect where they add to achieve extra output. Also, at tuning, most all the output is coming from the port, greatly reducing the excursion of the woofer. For this reason, vented enclosures can have a lot more output for two separate reasons. Not only because of the additional output from the port, but also because more power can be applied before reaching excursion limits of the driver. There is often a misconception that a sealed enclosure keeps a woofer from moving as far. That as you can see is incorrect.

Lets look at a PB12-4ohm in a 2 cubic foot enclosure. You can see in the sealed enclosure(purple curve) below it is reaching the 14mm Xmax at 35hz with about 700W input. Output is 111dB at that point. Once the vent is put in and tuned at 35hz(white curve), there is significantly more output. The level is already at 116dB at 35hz, a gain of 5dB already with no more power applied. Of most interest though is the decrease in excursion at 35hz. The woofer barely moves at that point. This is where the port is doing most of the work. 










This drop in excursion is really the "power band" where the most power can be applied without physically driving the woofer to excursion limits. This band is fairly narrow but when tuned properly and placed where it is most needed, allows for far more power to be input. In an SPL vehicle where only one small range needs to be played, this is a key factor. In this case from 49hz down it is affecting the excursion of the driver. The peak in excursion happens at 1/2 octave above tuning. This excursion peak is not going to be higher than the excursion would be from an equivalently sized a sealed box. It is however this peak that primarily determines the max input power before physically damaging the woofer due to over excursion. It is also critical to apply a high-pass filter to keep excursion under control below tuning.

A 6th order bandpass has the benefit of a second chamber being tuned. This gives a second point where excursion is brought down. When these tuning frequencies are close enough together, they can come together and bring down the overall excursion at all points between the two tuning frequencies. This gives the ability to put in more power over that entire operating range.










The biggest challenge with 6th order BP boxes is the change in parameters with respect to excursion. Of most importance is the change in BL. This is illustrated in the following graph. At rest and full BL value, you may see a fairly nice flat curve across the pass band as seen in the green curve. As Bl drops, that changes. A typical overhung woofer has a rated Xmax where BL has dropped to 70% of the rest value. In a sealed or vented enclosure, this has only a minor affect on changing the response curve. In a 6th order BP box though, it starts to change things more significantly. In the middle of the passband, there is already a 2dB drop in the output and peaks at the tuning points begin to get sharper (orange curve). If driven farther past this point to where the BL drops to 50% of it's rest it has a 5dB dip in the middle of the pass band and very pointed peaks above and below (red curve). 










This is why 6th order bandpass boxes can get so boomy at two points. The other issue is that the woofer doesn't stay at that reduced BL through it's entire stroke. As the woofer moves from rest, and comes forward, you see the change in the response curve. As it comes back to rest it changes again and then changes another time as it hits the excursion limits the other way. The result is a continually varying response curve with excursion. This is a huge factor in distortion. Inductance changing with respect to excursion also has an effect on changing the upper end of the response curve in a bandpass enclosure. Typical drivers have an S shaped inductance curve where inductance goes up on the inward stroke and down on the outward stroke. This curve is somewhat exaggerated, but illustrates the point. Green is the rest point. As inductance goes down on the outward stroke, the orange curve slightly increases at the upper end. As the coil goes inward and inductance goes up, the red curve drops on the top end. 










Add up both of these non-linearities causing the response curves to change, and it is easy to see why even a bandpass box that looks good in a model can seem to sound bad. Linear BL and linear inductance are more critical in a bandpass than any other box. Many cheap bandpass car boxes use woofers with short Xmax and no inductance control that are continually driven beyond their magnetic limits. 

Regarding isobarik alignments, in the following you can see what happens. BL itself doesn't change. Motor strength however does double. Motor strength is measured by using Bl^2/Re. Because 2 drivers are now used, Re is cut in half and Bl stays the same. Thus doubling Bl^2/Re for 2x the motor strength as expected. The other parameters also make sense. Cms is cut in half because it is 2x the suspension stiffness. As a result Vas is 1/2 also. Mms is doubled. The 1w/1m SPL is deceased 3dB but the 2.83V SPL is essentially the same due to the Re being cut in half.










John


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## William_White

That is a lot of information. You mention 6th order BP boxes but what about 4th order BP boxes?


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## Oliver

> Add up both of these non-linearities causing the response curves to change, and it is easy to see why *even a bandpass box that looks good in a model can seem to sound bad.* Linear BL and linear inductance are more critical in a bandpass than any other box. Many cheap bandpass car boxes use woofers with short Xmax and no inductance control that are continually driven beyond their magnetic limits.


If LOUD bad sound is what you are after ...

*"Tub Thump"* is beautiful when you want to show total strangers you can make a loud noise 

Make sure not to sound deaden the vehicle, that way you can have all sorts of nasty resonances - from your license plate moving(vibration)to rust falling off the car as it shimmies -n- shakes.

Use Rap or Hip-Hop recorded in an mp-3 format to extol ultimate ignorance in store parking lots near trailer homes


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## thehatedguy

Told you guys BL doesn't change...

The acoustic lever arrangement...it's a bandpass enclosure of sorts. You have an active driver in one chamber that is firing into another chamber that has 2 connected passive radiators- one small on the inside and a larger one on the outside (the one you see and hear).


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## Patrick Bateman

Wow I haven't noticed posts from John Janowitz in ages. Great info there - this is a great thread to bookmark.


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