The Objectives of a Loudspeaker in a Small Room

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.
"I try and excite the modes as much as possible which yields the smoothest response."

I'm surprised that you say that.

While exciting modes gives more output, they're widely spaced at low freq, giving a less smooth reponse.

Also it's a double-edged sword, along with peaks come nulls, albeit less problematic.
 
noah katz said:
"I try and excite the modes as much as possible which yields the smoothest response."

I'm surprised that you say that.

While exciting modes gives more output, they're widely spaced at low freq, giving a less smooth reponse.

Also it's a double-edged sword, along with peaks come nulls, albeit less problematic.


You have obviuosly not read my books as this concept is a corner stone to my room designs. I have studied the LF sound field in rooms since I did my PhD on this topic back in 1980. There is no question that exciting as many modes as possible yields a response with lower spectral variation than exciting fewer modes - this has been quantified in many publications - but in my books I go much further to discuss how to get good LF damping which spreads the modes increasing modal overlap and dramatically lowering spectral and spatial response variations. The net result of this room design and the use of multiple subs is by far the lowest spectral variation possible in a room of a given size.

This is not new stuff. You need to read more background material.
 
True, I have not read your books.

"There is no question that exciting as many modes as possible yields a response with lower spectral variation than exciting fewer modes -"

That's true at higher freq but how can it be in a normal sized room when the lowest mode is in the 20 - 30 Hz range?


"...good LF damping which spreads the modes increasing modal overlap and dramatically lowering spectral and spatial response variations. "

Is this true in anything other than a relative sense?

Because increased bandwidth from damping exists only in a mathematical sense; it only subtracts energy around the resonant freq, it doesn't move it to neighboring freq.

In which case it would be better to not have excited the mode in the first place.

My experience has been that the best, smoothest bass is outdoors, where there are no modes at all, followed by very large enclosed spaces, where the modal density is high even at low freq.
 
noah katz said:
True, I have not read your books.

"There is no question that exciting as many modes as possible yields a response with lower spectral variation than exciting fewer modes -"

That's true at higher freq but how can it be in a normal sized room when the lowest mode is in the 20 - 30 Hz range?



Its absolutely true - even more so at LF where the modal denisty is low. Above some frequency there are so many modes that the umber doesn't matter.

"...good LF damping which spreads the modes increasing modal overlap and dramatically lowering spectral and spatial response variations. "

Is this true in anything other than a relative sense?

Because increased bandwidth from damping exists only in a mathematical sense; it only subtracts energy around the resonant freq, it doesn't move it to neighboring freq.


My experience has been that the best, smoothest bass is outdoors, where there are no modes at all, followed by very large enclosed spaces, where the modal density is high even at low freq.

Again your intuition is wrong. Damping is REAL, its not just mathematics and there is a great deal of energy transfer from mode to mode when there is substantial modal overlap - this is a very critical point that is not often appreciated (see my PhD thesis).

Your point about outdoors is meaningless when one is restricted in room volume. Yes, in general, the bigger the space the better the bass. One has to compare bass approachs on a volume par basis. And why does a larger room have better bass? Because it has MORE modes not FEWER modes. Outdoors can be considered to be an infinite volume with an infinite number of modes - a continuum in Physics jargon.

These things are not at all intuitive, I assure you.
 
"More nodal sources all spread around the room. Artificially create the conditions of a big room. Use small subs."

The mode freq, which depend only on room dimensions, are the same regardless of how many sources there are.

"Again your intuition is wrong. Damping is REAL..."

Sorry, I was not clear.

Of course damping is real, and is in fact a good part of my livelihood.

A look at the family of curves for amplification ratio vs freq for different damping ratios (attached) will show that increasing damping reduces amplitude at *all* freq.

So increasing damping increases nothing but a number, and is why I balk when I hear of "mode spreading".

So I can't help but wonder if the improvements you achieved could be attributable to the lessening of objectionable modal response lumps and overhang, and might be further improved by eliminating them altogether.

"And why does a larger room have better bass? Because it has MORE modes not FEWER modes. Outdoors can be considered to be an infinite volume with an infinite number of modes - a continuum in Physics jargon."

It seems to me that if the the dimensions are infinite, how can there be any modes > 0 Hz.

Anyway, I'm keen on eliminating odd-order modes because it would get rid of my most objectionable (both audibly and measured) modes at 25 and 75 Hz, but perhaps the absence of the higher order modes would make the response ragged higher up where there would otherwise have been sufficient modal density.

An externally hosted image should be here but it was not working when we last tested it.
 
gedlee said:
Again your intuition is wrong. Damping is REAL, its not just mathematics and there is a great deal of energy transfer from mode to mode when there is substantial modal overlap - this is a very critical point that is not often appreciated (see my PhD thesis).

Let me make sure I understand this. Is this essentially the same type of behavior as that seen in weakly coupled pendula (or any SHO), but of course in a more general context? And the coupling between modes- is the reason this isn't seen in the non-damped picture because the modes are orthogonal which is no longer true when the boundary isn't rigid?


noah katz said:
It seems to me that if the the dimensions are infinite, how can there be any modes > 0 Hz.

I think this really depends on how mode is defined. If you understand mode as a standing wave that is formed because of the way reflections combine then if there are no walls sure there are no modes. But viewed in a more technical context, modes are eigenfunctions (and their frequencies the associated eigenvalues) of the Laplacian operator (or something more complicated if you are taking damping or other effects into account), and in this context it sort of makes sense to say that every frequency is a mode in free space. Maybe a more intuitive way to view this is to say that freespace is a room as each of the dimensions of the room goes to infinity. The frequencies of the modes then become continuous.

IMO though the second picture is a good example of a lack of rigor in physics allowing subtleties to go unnoticed; the associated spectral theory in this case needs to be modifed in order for things to make sense mathematically and this ends up explaining why in a practical sense we don't consider the solutions to be modes as we would in a bounded room.
 
"Maybe a more intuitive way to view this is to say that freespace is a room as each of the dimensions of the room goes to infinity. The frequencies of the modes then become continuous."

Not intuitive at all IMO; what sense is there in speaking of modes when there are no surfaces to generate them (there is the ground, but it takes two)?
 
My next experiment for "outdoor" bass in a small room will be the so-called "Double Bass Array" which I think was first tried in Germany and is starting to be used elsewhere.

Basically, you put an array of drivers on the front wall, locating them so the side wall, floor and ceiling reflections create an infinite planar array. With 4 drivers, you would put them at the 1/4 and 3/4 points between side walls and floor/ceiling. More drivers are better as they will play higher before C-C distance becomes a problem. Just keep the end driver to wall distance 1/2 the driver to driver distance. So, now we have a planar launch which eliminates side-side and floor-ceiling modes but what about the front-back modes. Simple! Put an identical array on the back wall, wire it out of phase and delay it by the time of flight equal to the length of the room. A pressure wave starts at the front wall, passes the listener where he hears it, and it simply dies when it reaches the back wall, getting cancelled by the out of phase and delayed drivers there.

Here's a thread by Nils at AVS and a 1/24 octave measurement. Pretty nice down low and it only starts getting ragged as the C-C distance gets too big. More drivers would fix that.

http://www.avsforum.com/avs-vb/showthread.php?t=837744

Edit: putting the pic in the next post to make this one more readable.
 
noah katz said:
"Maybe a more intuitive way to view this is to say that freespace is a room as each of the dimensions of the room goes to infinity. The frequencies of the modes then become continuous."

Not intuitive at all IMO; what sense is there in speaking of modes when there are no surfaces to generate them (there is the ground, but it takes two)?

Look carefully at what I said above. It comes down to how you define mode. If you define modes in the way you are suggesting, then there are none. If you define modes as the eigenfunctions of the Laplacian operator, then waves at all frequencies are modes in free space. These two concepts agree in a bounded room, but differ in free space. The construction I use above is a way to understand the second definition physically. What you should not be (but are) doing is looking for the behavior that defines mode to you in the free space case.
 
Rybaudio said:


Look carefully at what I said above. It comes down to how you define mode. If you define modes in the way you are suggesting, then there are none. If you define modes as the eigenfunctions of the Laplacian operator, then waves at all frequencies are modes in free space. These two concepts agree in a bounded room, but differ in free space. The construction I use above is a way to understand the second definition physically. What you should not be (but are) doing is looking for the behavior that defines mode to you in the free space case.


You are quite correct. The only way to find out the answer is to let the volume of a room go to infinity - what happens? There are an infinite number of modes, not 0.

Let me make sure I understand this. Is this essentially the same type of behavior as that seen in weakly coupled pendula (or any SHO), but of course in a more general context? And the coupling between modes- is the reason this isn't seen in the non-damped picture because the modes are orthogonal which is no longer true when the boundary isn't rigid?

Mathematically the system of equations for a room cannot be reduced down to a set of orthogonal functions unlesss there is a rigid boundary. Wall damping, or movable walls (like I build) do not allow for the modal wave functions to be orthogonal. This is nothing more than the mathh telling us that the modes couple. The greater the overlap (the more damping there is) the greater they couple. People just don't seem to get the significance of this fact (some don't even recognize the fact).

I did my PhD in small room LF modes and in that thesis I found that modal interaction was more significant than room shape in forming a smooth room response. Thus, if the room is damped well enough, the shape doesn't matter (at LFs). This is a kin to saying that the mode shape, type, location, whatever, doesn't matter if the room is damped well enough. Tough to do (LF damping) though - read my book for how it can be done.
 
noah katz said:


A look at the family of curves for amplification ratio vs freq for different damping ratios (attached) will show that increasing damping reduces amplitude at *all* freq.

So increasing damping increases nothing but a number, and is why I balk when I hear of "mode spreading".

[/IMG][/URL]
Again, your example is incorrect. You have shownis a Low Pass electrical function, not a room mode simulation. Its not applicable. If you do a real room mode simulation you would see that as the damping increases the modes spread in width and overlap each other. "Mode spreading" is the correct and applicable term for the effect so you shouldn't "balk" at it.
 
"What you should not be (but are) doing is looking for the behavior that defines mode to you in the free space case."

Why should I do that when my speakers are in a room and not in free space?

And again, I cannot fathom what connection to reality the mathematical prediction of infinite modes has absent the mechanism of generating *any* modes.

"Mode spreading" is the correct and applicable term for the effect so you shouldn't "balk" at it."

OK, maybe I needn't, if I was mistaken in thinking you meant that energy was transferred from the resonant freq to neighboring freq.

Though upon further reflection perhaps that's possible in a 3D acoustic situation vs. the single degree of freedom mechanical, which as Dr. Geddes noted is analagous to an electrical LP filter .
 
noah katz said:

And again, I cannot fathom what connection to reality the mathematical prediction of infinite modes has absent the mechanism of generating *any* modes.


Perhaps it helps to distunguish between the rough idea of a "resonance" and the precise, mathematical "normal mode".

An observed resonance will involve vibration of speaker, air, walls and also involve loss - as the air moves around, leaks out and otherwise produces heat.

The resonance, at low enough frequency, will be approximated in frequency and in sound pressure distribution by one normal mode of a box the rough size of the room, filled with air. (Found as a formal solution to the appropriate equations, with or without considering some average frequency dependent or independent loss factor to set the Q of the modes.)

If, however, you wanted to fully understand your observed resonance as the normal mode of a system, that system would have to include everything in your room that is vibrating at the mode frequency (walls, strands of carpet etc.). Because that is impractical, we use the simple "box" normal modes as the basis, and explain what is observed by using mixtures of the modes (that are normal/orthogonal in the model system).

The trick is to remember that the resonances are not really the normal modes of the "box" and so won't behave the same if considered in too much detail. The most significant difference has already been alluded to: the walls are part of the system and couple what would be normal modes of the box (open doors, leaky windows, large furnishings etc. also have similar effects).

Using a modal basis to approximate a different physical system often leads to confusion (but is still much better than nothing, given how hard it is to solve the full problem).

The idea of a continuum of modes in an unbounded system arises naturally from the mathematical model (and as you know is not such a bad model in a real room at high enough frequency). A continuum of modes is a very useful concept in several areas of physics. It is, however, probably a bit of a distraction to worry about it in the case of low-frequency room modes for all practical rooms.

I hope that helps a bit.

Ken
 
Thanks for the effort, but not really.

I get that in the limit, moving walls apart gives an infinite number of modes, but I can't make the leap to that being the same as no walls.

Rereading, I guess you weren't even addressing that, which is fine, as it's wandering off topic.

"we use the simple "box" normal modes as the basis, and explain what is observed by using mixtures of the modes (that are normal/orthogonal in the model system)."

Might this be related to mode spreading?
 
noah katz said:
I get that in the limit, moving walls apart gives an infinite number of modes, but I can't make the leap to that being the same as no walls.

I'm tired so I hope this makes sense:-
it is a bit pointless to answer your "no walls question" without the math, I'd say don't worry until you need the solution. Or perhaps it suffices to say that very very far away from any wall it is hard to tell if there are walls at all (unless you try with a very very long wavelength). Perhaps I misunderstand your difficulty.

As was mentioned above damping makes modes broader, but they would still be separate unless something coupled them to allow energy exchange among them. Walls flexing would be a good example of such a "coupling" whereas weaker coupling could be due to e.g. diffraction at furniture or features of the room shape. The more the modes overlap the easier it is for energy to pass from one to another (the frequency of the sound does not change of course).

If the coupling among modes is "very weak", the rigid-box mode picture remains close to the truth, but if the coupling is "too strong" the approximate modes are too far away from the true solutions to be of much help in understanding the problem. I've seen both cases in reasonably usual "small rooms".

I'm not sure I'm helping here ... it is quite a large topic.

Ken
 
kstrain said:

As was mentioned above damping makes modes broader, but they would still be separate unless something coupled them to allow energy exchange among them. Walls flexing would be a good example of such a "coupling" whereas weaker coupling could be due to e.g. diffraction at furniture or features of the room shape. The more the modes overlap the easier it is for energy to pass from one to another (the frequency of the sound does not change of course).

Ken

Mathematically any boundary condition at the walls that is real, i.e. damping. will cause the modes to be NOT orthogonal, i.e. mode coupling. This FACT is usually ignored as for low damping since it is a small effect. But in any decent listening room the damping is high enough that there is strong modal interaction. Hence the non-orthogonal modes situation has to be considered as the norm and the weakly coupled orthogonal modes situation as a "special case".

There simply is no question about the limiting effect of a room becoming infinitly large and the modal density going to infinity. This effect is completely analogous to the wavenumber spectrum in optics where in free space it is a continuum with an infinite spectrum of wavenumbers and in lenses and aperatures it becomes discrete yielding the diffraction effects of these devices. This analogy is completely correct and often used in Physics, so lets not agrue about it anymore.
 
Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.