I thought that the dampening was meant to reduce boomy-ness in the cab by reducing reflection off the back panel?
No. Damping material controls reflections, not boom.
Boom is the result of a too-high Qtc caused by running the driver in a too-small internal volume.
Hollow-core polyester fiber fill controls boom by reducing the Qtc by making the box acoustically 'larger' by
Stuffing the box.
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This chart shows the Eminence BP102-8 Qtc in various sealed box volumes.
Note how the Qtc increases as the box volume gets smaller.
The Qtc=1.5 has a noticeable boom in the 150 Hz range.
The intent of damping material is to absorb short wave lengths that would otherwise cancel internally after being reflected from an opposing wall.
The Allison Effect is a cancellation (suckout) that occurs from a 180 degree out-of-phase reflection from a wall.
(Allison, Roy: "The Influence of Room Boundaries on Loudspeaker Power Output." JAES, June, 1974)
For example, you have a cab that is 11.5" deep from the speaker cone to the closest wall.
11.5" is one-quarter of a 3.83 foot wave length, or (1128/3.83) = 294.5 Hz.
This frequency will cancel due to the Allison effect.
Reflections bouncing around inside the cab will vary in wave length depending upon where they reflect in the cabinet.
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Notice the nasty response pattern in this raw sweep of an unlined cabinet.
That's why bracing has the same effect as dampening, no?
No.
Bracing prevents panel vibration (buzzing).
Acoustic power is wasted when expended on making the panels buzz.
Also, doesn't dampening need to be placed on half of the walls, as in, for each wall that faces another, one of the two is covered?
Yes, at a minimum.
When all reflective surfaces are covered, more control is exerted over high frequency reflections.