The diaphragm is a sheet of fairly rigid material that you are mechanically pushing forward and backward rapidly at a low frequency. That movement is pushing and pulling on the air, creating pressure waves in the air. You know, sound! Think of a speaker. The cone is the diaphragm. The coil and magnet drive it forward and backward at a frequency, creating sound in the air.
In an acoustic guitar, the top is the diaphragm. The movement of the strings causes the bridge to bounce up and down, which makes the top bounce up and down. When the top bounces up, it directly pushes the air toward you. When the top bounces down, it squeezes the air in the box and squirts some of it out toward you.
Same thing with an upright bass. The flexing of that huge top is throwing air right at you. Plus secondary air is getting squirted out the F-holes.
The sound is coming from the flexing of the diaphragm. And, the lower frequency you want to create, the more volume of air you have to push with the diaphragm. You need a larger diaphragm, with more square inches of area. Or, you need to give the diaphragm more distance of travel. Or both.
You can get low frequency out of a small size diaphragm. Look at 6" sub-woofer car speakers. The trick is to have really long travel. Those little speakers can kick a half inch.
Think about how this applies to designing a RABG. To create LOUD LOW sound, put your engineering effort into getting a lot of travel out of the diaphragm, rather than making the volume of air in the box really big. Make a reasonable size box with a top that can really move.
Something that's often misunderstood: The main reason why the body of an upright double bass is so big isn't to create a box with a large volume of air. It's to create a large diaphragm, in square inches, on the front that can flex a lot. Thin wood has mechanical limitations on how much you can bend it back and forth repeatedly without it breaking. Making the diaphragm larger allows the center to deflect farther without bending the wood as much. The wooden top of an upright bass is big so that it can flex a whole lot without shattering.
The big volume of air in the box means something too, of course. The natural resonance of the air in the box depends on the volume (cubic inches) of air space. Larger volume equal lower resonance frequency. Tuning that is a part of boosting the sound of a stringed bass instrument.
But that's a secondary effect to work with. The main thing that creates the sound is the movement of the diaphragm.
Here's an example of a moderate size diaphragm, with a lot of travel, and no real air box behind it. It makes deep loud sound similar to an upright bass.
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