if using 1" thick MDF,,is internal bracing still needed?

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When we consider just subwoofers, box wall "ringing" at several hundreds of Hz or kHz range is not an issue (looking at danny_66's link). The problem is ballooning with sound pressure which causes all kinds of vibrations and distortion peaks.

Traditional and proven way to make a good bass cab is to use bracing, it is effective against ballooning. Wool or lining are not needed, with the exception of filling sealed cabs to get a little higher Q.

Lamination is the best way to make a good full range speaker's cab, and add bracing there too! Inside should be lined or filled too.
 
Well missing from the study at least the translated version is what is the input signal going into the box? If you use a ported design the over and under pressure is not what is being modeled here (sealed box).

If the experiment was to use a pink noise generation with a narrow bandpass of what actually frequency would being developed in a sub-woofer I would concur that the data points to better bracing however it does not.

Also of note in secondary output could be measured with a contact sensor on each panel to see how much engery is be loss through the side and back walls of a box.
 
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