"How does the area of the soundhole change the sound of an acoustic guitar?"
Partly by altering the pitch of the 'main air' resonant mode.
Think about the sound you get blowing across the mouth of a wine bottle. That's called a 'Helmholtz resonance': there is a sort of 'piston' of air in the neck of the bottle that's bouncing on an air 'spring' inside.
You can get a similar sort of resonant mode going on a guitar, although you really have to blow across the hole with a shop vac to get it clearly. The thing is that what you hear on a guitar is _not_ really a Helmholtz mode, because that requires a rigid vessel. The flexibility of the top and back of the guitar influence the pitch of the air moving in and out of the hole, and the air, of course, also pushes on the top and back, which alters their pitches from what they 'should' be. In fact, in the low range, you can think of the guitar as a 'bass reflex enclosure', but a pretty complicated one compared to the speaker cabinets you buy.
The size and location of the soundhole and the size of the body sets the pitch of the _Helmholtz_ mode; what you'd hear if the top didn't move. The smaller the hole and the closer to the upper end, the lower the Helmholtz pitch. Generally speaking, the corresponding air mode (which we often call the 'main air' resonance) will be at a lower pitch than herr Helmholtz would have predicted, due to the effects of the top and back.
The 'main air' mode is the lowest pitched resonance that can actually reinforce the tone of the instrument. It's usually around G on the low E string, so it gives you a lot of the low-end power and fullness. It can also contribute to the infamous 'wolf', but we'll skip that for now.
Punching another hole in the box will raise the Helmholtz pitch, and thus usually also the 'main air' resonance. It's not just a matter of equivalent area, though; the further from the main soundhole the port is, the greater the effect on pitch for a given size port, in general.
What effect this will have on the tone of the guitar is harder to predict. Opening the port can (but does not always, I think) increase the output of the guitar as a whole in the 'main air' mode frequency range, so that would tend to make it sound 'bassier'. However, it also raises the pitch, which makes it 'less bassy'. How the balance works out in any particular case is something that can't be predicted, partly because it's largely subjective. If you think it's 'better', then it's 'better' for you. I might not agree.
There are a couple of other effects from enlarging the main soundhole, too, and others still from putting in a port, but that's enough typing for now. You asked a longer question than you thought!
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