Which is better for a DBA (Swarm); powered subs or unpowered?


I want to start building a swarm (starting with 2 subs), on a budget.  Starting with $1000, am I better off buying two used powered subs, three less expensive used powered subs, or a subwoofer amp (eg Dayton SA1000) and two (less expensive) used unpowered subs?  What is the advantage of having a discrete subwoofer amp?  Room size is 13'x22'. 
128x128cheeg
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An ambient recording in one made in an acoustic space that is not treated do remove all reflections and does not have additional reverb added.

Like a pipe organ in a cathedral.
ieales
... Sound waves do not interact and sum ...
Actually, they can sum, and they can also subtract. Using out-of-phase signals, for example, is how active noise reducing headphones work. Phase is also part of why LF signals can be directional.
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Ieales wrote:

" DBA proponents are not charlatans, but neither are they correct as the the ability it to produce time coherent bass. "

Arrival time coherence in the bass region is not critical, but decay time coherence in the bass region is.

The ear is incapable of even registering the presence of bass energy from less than one wavelength. And the ear is incapable of registering pitch from less than several wavelengths. This from a Journal of the Audio Engineering Society paper which I no longer have access to.

So the ear simply does not have enough time-domain resolution in the bass region to detect arrival time differences of a few milliseconds.

So let’s look at the decay times. The longer a sound lasts, the louder it is perceived to be. So bass frequencies which take longer to decay sound louder.

Also, since speakers + room = a "minimum phase" system at low frequencies (according to both Floyd Toole and Earl Geddes), when we know the frequency response, we know the time-domain response. Thus is it the peaks which take longer to decay into inaudibility. This implies that the frequency response is particularly important at low frequencies.

Which indeed turns out to be the case. If we examine a set of equal-loudness curves, we see that they bunch up south of 100 Hz, such that a 6 dB change at 50 Hz is perceptually comparable to a 10 dB change at 1 kHz. This in turn implies that improvements in the frequency response in the bass region pay subjectively large dividends.

In other words I believe that a good distributed multi-sub system addresses the issue that matters the most to the ears; namely, the in-room frequency response.

Ieales again: "By FAT I mean that unless time correction is implemented the separate sub signals will arrive spread over several milliseconds...

"IMO, it’s as unlistenable as MP3...

At RMAF 2017 we displayed using a distributed multi-sub system in one of the standard (small) hotel rooms. An industry veteran cable manufacturer, with several decades of experience, handed us his thumb drive and asked us to play a recording of Fanfare for the Common Man. When it was over, he told us that was the most natural rendition of the tympani he had ever heard in any room at any audio show. He said it sounded just like what he heard when he went to a concert.

(Incidentally in my experience the term "fat" is normally associated with a frequency response peak and its attendant long decay time, so it IS a time-domain issue - but applicable to the DECAY behavior, not the ARRIVAL TIME behavior.  Our ears cannot react fast enough to hear "fat" in the arrival of bass energy).  

So I’m going to go out on a limb and claim that Ieales’ statement that a distributed multisub system is "as unlistenable as MP3" is an exaggeration. If he wishes to prioritize arrival time that is fine with me, we have a difference of opinion on that subject.

Duke