Post somewhat late vs what was mentioned before, still better late than never...
JBL Engineers Mark Gander and John Eargle did a study on loudspeaker arrays performance. An interesting aspect of this study is summarized in Eargle's Loudspeaker Handbook 2nd Ed. They noted a downward shift of vented boxes tuning frequency when increasing the number of LF cabs together. The box group down tunes (self-downtuning!) when they're multiplied. Also worth noting, Eargle added in his book the mention of a possible woofer displacement overload, not seen in the original article, caused by an unusual cone excursion limitation.
The experiment involved ground plane measurements of the same LF enclosure but the number of them varied. One cab Fb 31 hz to start with, always doubling their number, going to two of them, then four, finally eight boxes (in Eargle's book its limited to 4 boxes). The tuning frequency, as measured by the impedance null for system resonance, was recorded for each test. Result: for each doubling of cabs the group's tuning frequency went down by 2 hz, so it would be a 6 hz shift in Fb for 8 cabs in a stack.
Initially doesn't seem like a big tuning shift but it could end up being problematic, and knowing that down tuning puts more strain on a woofer. Consider a user having down tuned 2 or more pairs of boxes to achieve extended LF reach, then stacked them... Might be like running towards a cliff, not knowing its there. The unsuspected issue is driver Xmax may not be reached first where one would expect (VLF) but instead somewhat higher in the spectrum (LF). With low power this may not appear as an issue, whereas at higher drive level cone travel limit might be reached unexpectedly, specially for older and limited woofer models (with the increased distortion included).
The stacking process for LF boxes leads most of the time to mutual coupling of these (drivers closely spaced), its well known and purposely used in order to increase bass output, in addition to saving floor space on stage or at home. Here its not so much the frequency response we're concerned about, its rather the driver's acoustic output capability which may be somewhat compromised. Its another, but less known, aspect of mutual coupling.
Little explanation is given as to why this box tuning shift of stacked vented LF cabs takes place, except for this mention in the original paper: "The downward shift is caused by mutual coupling increasing the radiation reactance." (Gander & Eargle, JAES, 1990, P.214)
The risk of using enclosures actually tuned lower than driver Fs may exist too.
* Have to reorganize the rest of this post (already written) due to pic files size. Next part to follow shortly.
Richard
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