Resonances
The guitar is a complex beast with many resonances that are determined by the thickness and stiffness of the wood.
The lowest resonance is different - it's a Helmholtz resonance - the same resonance that is excited when you blow over the top of a bottle - the resonance comes from the springiness of the air in the bottle and the weight (mass) of the plug of air in the neck. As the plug is sucked upwards as you blow over the bottle, the air in the bottle is expanded, and sucks the plug back in. It overshoots, compressing the enclosed air which pops it back out. The plug of air vibrates at a frequency that depends on the plug mass and the amount of air in the bottle that gets compressed.
The Ocarina is the only musical instrument based on this principle, and the sound is pleasingly sweet.
What does this resonance mean for a guitar? Above this resonance, which is usually around bottom G#, the guitar radiates well. Below it, it radiates less well.
Loudspeakers
Anyone who has heard a loudspeaker out of its box will know that there's no bass. When the cone moves slowly, as it does on low notes, the air simply spills over the edge of the speaker and disappears round the back to fill the void.
A simple loudspeaker box is a sealed box or "infinite baffle" that prevents the back wave and front wave from meeting and cancelling out.
A sealed box is cheap to make and its performance is easy to predict.
The problem with such a box is that unless it's large, the sealed air is so springy that the speaker cannot drive the air with enough excursion to generate deep bass.
Enter the ported speaker cabinet! By adding a Helmholtz resonator - a plug of air - the box can radiate sound too.
Doesn't the back wave leak out and cancel out the bass, just as if there was no box present? Well, yes it does, but only below the Helmholtz resonance. At the Helmholtz resonance, the air coming out of the port comes out in the same direction as the loudspeaker cone.
Below the Helmholtz resonance, the speaker and port act like two trampolinists bouncing alternately on the springy air in the box. At resonance, they act like two trampolinists bouncing together. In the case of a loudspeaker, it's like having a second loudspeaker join in - much more bass. There is a formula (the Thiele-Small formula) that lets you calculate the size of the port so that you can tune the resonance as you want.
Applying this to a guitar
A loudspeaker cabinet is designed to be as rigid as possible, guitars are not. Indeed a rigid (laminate top) guitar has poor bass.This is because the entire front of a guitar fulfils the role of a loudspeaker cone. Above the Helmholtz resonance, air comes out of the soundhole as the top moves outwards, and reinforces the sound. Below resonance, air goes into the soundhole as the top moves outwards, and the bass is cancelled out.
On our contrabasses, the high resonance (an octave below the bottom note) means that the whole bottom octave is thin because the soundhole is hindering rather than helping.
The Tornavoz
Luthiers, notably Torres, experimented with a Tornavoz - a conical brass fitting inside the soundhole. Being larger than the soundhole, it required fitting during construction, and its removal wasn't easy either! Its purpose was evidently to focus and project the sound, but our MD has a suspicion it might also have improved the bass on a small bodied guitar. It might, therefore, improve noticeably the deep bass on a big guitar...
Time to revisit the Tornavoz!
Port Design
The soundhole on a guitar is like a port on a loudspeaker - lengthening the port by adding a tube inside the guitar will lower the resonance.
Since the top is only a few millimetres thick, surely a port can easily drop the resonance an octave?
But no...
Although the soundhole is very thin, the air passing through it has an inertia that makes it behave as if the soundhole were quite a lot deeper - think of when you blow out a candle - the air passes through your lips but stays in a tight stream for quite some distance. So in reality, adding a port does not lower the resonance quite as much as we hope. But it's definitely worth doing!
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