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Putting an accelerometer on the wall of a cabinet is not a reliable indicator of the audibility of a resonance (sorry John Atkinson). For example, some panel resonances radiate sound effectively and others do not, but both exhibit vibration at a point on the panel. Harman and other advanced designers use scanning laser vibrometers to reveal patterns, polarity and amplitude of panel movement which guides the placement of structural reinforcements to reduce acoustical radiation from the resonance. When it is below the audible threshold in the anechoic frequency responses all is well (see the paper, or my books). It is not necessary to have foot thick concrete enclosures to eliminate audible resonances, good engineering can do it in rectangular wooden boxes.
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