I must have hit these points earlier in the thread, but I'm not going to take the time now to dredge it up.
First: 'loudness' is a
subjective impression which is actually very hard to relate to
power in a general way. Large guitars tend to sound louder, particularly to the player and folks close by, but it's easier to make a powerful small guitar, and the sound teds to 'carry' better out in front.
The reason it's easier to make a powerful small guitar is that the power output is a function of the relationship of the vibrating area of the top (mostly, the lower bout) and the mass. A higher A/m ratio produces more sound. As you enlarge the box, increasing the span of the lower bout, the stiffness drops assuming the same top thickness and structure. At some point it tends to fold up due to bridge torque, so you have to beef up the structure. This adds weight, and the weight goes up faster than the vibrating area, so the ratio of A/m goes down.
Large guitars have an advantage in producing low pitched sounds, partly because of the larger area of the top, but mostly because they can pump a larger volume of air through the hole. Low pitches tend to radiate in l directions about equally, so the player hears them as well as anybody in the room. High pitches tend to go off the top and out of the hole toward the audience, so a small guitar is radiating most of it's sound outward, and the play doesn't hear it as well.
It's all physics, as the guy says, but it's pretty complicated physics, and not altogether obvious. There may also be subjective effects. For example, we all know that big dogs bark at a lower pitch than small ones, and big dogs are more powerful. When we hear that low pitched 'bark' from the Dreadnaught we tend to assume it's more powerful. TYat may not be the case.
