Multiple Small Subs - Geddes Approach

[gedlee]

But I thought that we had decided that the LF modes were at least "nearly" MP. In which case what you describe wouldn't apply.

All that you say is well know but I'm still not sure that I follow the connection to the discussion at hand. Decay rate only has a meaning for non-steady state signals.

[Tubamark]

Sorry to interrupt the MP debate. Perhaps a new, but plenty on-topic thought for discussion will be welcome:

I will be sampling the Geddes multi-sub approach soon (when my new nicely-damped listening cave is complete), but initially using dipole mains, rather than monopole mains as assumed in the discussion-to-date. Sub 2 will be a modest IB located above wall midpoint, Subs 1 and 3 boxed. Dipole mains strong down to ~50 Hz, so they are certainly IN da mix.

As I grasp the concept, my application of the method should be unchanged, regardless of the radiating pattern of the numerous sources, Correct? --place mains where they "work" best, then Methodically optimize/dial-in the subs in succession -- the METHOD accounts for whatever actual phase and modal excitation issues occur with any given setup in the room, so source radiation pattern (below Schroeder freq) is MOOT.

Comments? Detractors be gentle - I'm recovering from hernia surgery this week . . .

--TubaMark

[soongsc]

would be interesting to know what kind of music you listen to. Posting covers of CDs and LPs used for listenign tests is a given when they are serious. Most of the time when we see the cover, we know if we have it in our collections.

Normally hernia takes about a week to recover, so probably the hard stuff next week.

[mat02ah]

Originally posted by gedlee
But I thought that we had decided that the LF modes were at least "nearly" MP. In which case what you describe wouldn't apply.

Exactly. That's the point.

With your approach you are optimizing the amplitude response. Since the speaker-room system is MP at LFs, you are optimizing phase response and the transient response as well. That's why your approach is useful. If the system wasn't MP at LFs, your approach probably wouldn't be useful.

The only point we seem to disagree upon is the usefulness of the MP concept for the problem at hand.

[soongsc]

Room reponse cannot be minimum phase if we assume the source image method to be a valid way of describing reflections.

[mat02ah]

Originally posted by soongsc
Room reponse cannot be minimum phase if we assume the source image method to be a valid way of describing reflections.

I don't think it's a valid way if the wavelenghts are not notably smaller than the dimensions of the room. The source image method works like ray optics. For ray optics the wavelenghts have to be significantly smaller than the dimensions of the objects involved (mirrors, apertures, slits, ...).

At LFs in small rooms (that's what we're talking about here, right?) the wavelengths are not significantly smaller than the dimensions of the room.

[Russell Dawkins]

I've often wondered how this relates to the audibility of deep bass in very small spaces, like automobile interiors.

[john k...]

Originally posted by mat02ah


This exactly is why I (and others ...) thought (and still think) that the speaker-room system can considered to be MP at LFs.

It doesn't hold. MP is not valid at low frequency. Here is a series of figures based on simulation where we can control which modes are included constructing the SPL response at a point in a room.



The top three response plots are each for the case where only the DC mode and a the first axial mode in either the x, y or z direction are included in the response calculation. In all three cases the response is reducible to a MP response as is indicated by the thin blue line overlaying the thicker green line. The thicker green line is the computed phase of the response and the thin blue line is the MP corresponding to the amplitude.

Now look at the bottom three curves. In this case the response is composed of the DC mode, the first axial mode in each direction, the first three tangential modes and the first oblique mode. All these modes result from consideration of the DC mode and combination of the first axial mode in each direction. At the left we see the amplitude response in violet, the computed phase in green and the MP corresponding to the amplitude in green. The second curve shows the phase of the all pass component of the computed response curve, and the phase which would result if the all pass were a constant delay with the first wrap in phase occurring at the same frequency as the all pass phase. It should be apparent that the all pass phase is not a pure delay. The third figure on the bottom right is a plot of the reconstructed in room response found by multiplying the MP response times the all pass response. As you can see, it is identical to the green phase shown at the left.

What this shows is that even when only the very low frequency modes are considered the response is still not MP at low frequency. There is a highly nonlinear, non MP component to the phase. The only way for the in room response to be reducible to MP (that is, MP plus a pure time delay) is to have the listening position very close to the source. In such a case the direct sound dominated and if the direct sound is MP then the sound at the listening position can also be MP, though it won't necessarily have the same amplitude as the source. Think of it like this; very, very close to the source we would measure the radiation of the source (a near filed measurement). As we move the measurement point away the relative strength of the reflected sound increases. At first this only introduced ripples in the response which remain MP. However, as we move further away for the source the relative strength of the reflected sound may start to dominate the response and there is a departure form MP.

I started putting this together last night but didn't get to post it until this morning so I guess there are several posts in between.


Just another brief addition. You must also consider that the contributions from different modes can also be inverted in phase depening on the sign of the eigen function of that mode at both the source ans listener position. So the sumation over many modes means many in and out of phase contributions.

[mat02ah]

Originally posted by john k...

It doesn't hold. MP is not valid at low frequency. Here is a series of figures based on simulation [...]

What simulation? How was it done? Your own software? What conditions were used, what assumptions were made? You certainly don't expect anyone to accept these barely readable screen shot cut-outs as proof of anything, do you?

How is this simulation going to look like, if you simulate multiple subs (either the randomly placed for best amplitude response or symmetrically)? Will your simulation show the same improvements the measurements show?

Originally posted by john k...

There is a highly nonlinear, non MP component to the phase.

Where does this non-linearity come from? Why is the superposition principle not valid here? This is where you could convince me.

edit: Quote from your web site: "We must recall that the in room SPL can be considered as being built from sum of the responses of the excited modes."
So you're considering this to be a linear system.

How can the summation of modes that are MP be non-MP?
Or are some of the modes you included (tangential or oblique ones) non-MP by themselves?

If the speaker-room-system is not MP, then looking at a steady state amplitude response as Earl suggests shouldn't be enough to optimize LF performance. Are you saying that? Or are you saying that phase and transient response don't matter at LF?

[soongsc]

Originally posted by mat02ah


I don't think it's a valid way if the wavelenghts are not notably smaller than the dimensions of the room. The source image method works like ray optics. For ray optics the wavelenghts have to be significantly smaller than the dimensions of the objects involved (mirrors, apertures, slits, ...).

At LFs in small rooms (that's what we're talking about here, right?) the wavelengths are not significantly smaller than the dimensions of the room.

As long as one dimension is longer than the wavelength of interest, then there is a mixture of non-minimum phase which makes the whole analysis and measurement non-minimum phase.

If anyone can tell by what criteria room response can be considered minimum phase, then we can face the issue in a very clear technical approach.