It would be great if there were some simple way to predict what all the resonant frequencies of the comppleted box would be before you glue it up. It's SO much easier to get at stuff when it's on the bench, rather than having to reach in through the hole! Sadly, the very complexity of response that makes the guitar interesting to play also makes it very hard to predict what's going to happen. I have seen computer models that can give you a good idea of what the modes will be, but they're complicated to use, and only put the problem back a step or two. To get useful results out of them you have to be able to measure the wood properties very exactly, and that would take a lot of effort in itself.
In the low range the guitar acts as a 'bass reflex enclosure' with flexible walls. If you look this up in a book on speaker cabinets, you'll see that the ideal BRE has rigid walls, high damping for both the speaker cone and the air resonance, and the cone and the cabinet pitch are the same. Physically, this is a mechanical analog to the 'Butterworth' filter circuit, in which two L-C networks with the same properties are linked, but the speaker setup uses high damping where the goal in the electronic case is usually low damping.
With two resonant elements tuned to the same pitch you'd expect a single tall, narrow peak, but that's not what happens. Instead since it's impossible to ever have two things exactly alike, the resonant pitches of the two elements will always be slightly different, and that's enough of an opening for one of them to change phase relative to the other and start soaking up power (in a sense) rather than putting it out. The output of a Butterworth filter thus actually will have two peaks, with a dip in between, and it will fall off very quickly on either side. With care, you can have something approaching a 'square' response curve, with little output below or above selected values, and a fairly high, and nearly uniform output between. This makes it a good narrow-band filter.
In the case of the speaker cab, the high losses make the output less 'peaky', and the dip in between the two peaks you do have is shallow. The output rises pretty fast as you approach the resonant band, stays within 3dB of the peak height over a wide frequency range, and then falls off fairly slowly, so that it takes it a long time to drop 3dB below the peaks. Since a 3dB change in loudness is barely audible, the response curve of the speaker is fairly 'flat' over a wide band. It's also much more efficient than an 'infinite baffle': the box and port capture some of the energy from the back of the speaker and put it out in front.
On the guitar the 'real' Helmholtz pitch, and the 'real main top' pitch are not the same: often they would be about 6-8 semitones apart in isolation. They are, however, strongly coupled by pressure changes inside the box, and one outcome of that is to shift the pitches. The stronger the coupling, the more the pitch shift, so box depth and hole size get into the equation: a larger hole or a deeper box gives less pressure change for a given top amplitude, and thus less coupling. Thus when the 'Helmholtz' mode starts out around, say, 125 Hz, it can end up at more like 98 (G). I've seen it anywhere from 87 (F) to 233 (A#) on 'standard' gutiars with 'normal' soundholes. Similarly, the 'main top' mode, which might be around 180 Hz without the air coupling, can end up at more like 196 (G). Note that the air mode, I think because it involves moving less mass, shifts more in pitch.
There are various ideas about what the 'right' pitch is for these modes on the completed guitar, and why a particular pitch is 'right'. In a broad sense, I like to have the 'main air' pitch within a third or so of the lowest note on the guitar in normal tuning (whatever is normal for that guitar). The 'main air' mode fills in a lot of the fundamental of the lower notes. If it's too low, then you don't get the benefit very far up the string, and if it's too high, the lowest notes sound 'thin'. I like it between F# and G# for the most part.
It's even harder to give a fast rule about the main top pitch. In part, of course, you're sort of stuck with what you get when you make the top stiff enough not to fold up. Many people do caution against having the 'main top' pitch right on a played note, say the open G string. This is because top motion at this frequency (and the 'main air' pitch as well) can react back on the string and shift the pitch, or suck the energy out too fast, giving a 'wolf' note.
It gets more complicated when you factor in the back. In a way you can think of the back in the low ferequency range as an extension of the top area: if the 'main back' tap tone is anywhere near that 'mian top' pitch the two will couple. This has the effect of dropping the 'main air' pitch (the air has to move the back as well as the top, so the pitch is dragged down) and making the air resonance stronger. Even the sides can get into this act, so you can see why it's hard to calculate.
Anything that makes the top or back more flexible will tend to drop the 'main air' pitch. It turns out that loosening the top in the middle, by using scalloped braces, is more effective than loosening the edge. Apparently the top is a larger 'equivalent piston' when the center is flexing. Scalloped bracing also drops the 'real main top' pitch, so that it's closer to the 'real Helmholtz' pitch, and this makes the coupling stronger, which, in turn, causes a larger pitch shift (did I mention that the total pitch shift is a measure of the coupling strength?).
Making the body deeper drops the 'real Helmholtz' pitch, but it also decreases the coupling strength all else equal. The upshot is that the 'main air' frequency stays about the same (lower to begin with but less shifted down), and the 'main top' pitch can drop (same pitch to start with, but less shift upward). This seems counterintuitive until you understand the physics.
A larger soundhole in the same place raises the 'real Helmholtz' pitch, and decreases the coupling, so that the 'main air' mode can end up higher in pitch, and the 'main top' lower. Usually the top shifts less, again, because it's heavier.
And so on.....
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