An empty vessel most generally makes no noise at all, just like a filled (or solid) one. How much noise it makes depends on the strength of the abuse applied.

For empty tubes, like flutes and whistles, how hard you blow is the main determinant of how loud they are.

For bars, like xylophones or harmonicas/reed instruments, it's largely a matter of how hard you whack them, or for the reeds, how hard you blow.

For most string instruments, the sound that leaves the instrument and is heard depends on how much movement you can generate in some large surface that can push a lot of air. For things like a guitar, or fiddle, the surface most effective is the top plate of the instrument, but the loudness depends largely on how much the string is stretched when you turn it loose.

The "vessel" volume of the instrument body can have a resonant frequency for the air inside. That frequency is fairly accurately given by the Helmholtz equation that says that the resonant frequency of a partially closed volume is proportional to the total area of all the holes, and inversely proportional to the volume of the air space inside. You can lower the resonant frequency by using a bigger air space, or raise it by using larger (or additional smaller) holes. BUT IT IS NOT THE AIR MOVING IN AND OUT THROUGH THE HOLES that is the most significant source of the sound you hear.

For most string instruments, the top plate, which can also be "tuned" to have one (or more) favored frequencies, is the main thing that pushes the air to produce most of the sounds you hear.

The top plate is connected to the air space, and if the two characteristic frequencies are "close enough" inward motion of the plate can compress the air inside so that the energy of the vibration is stored up in the air to push the top plate back up, to where the plate can move the outside air without losing much of the energy.

This "storage and return" effect can fail if the two frequencies are too far appart, but a small difference in the two frequencies can greatly extend the frequency range over which "about the same" acoustic volume (noise) is transmitted to the external air for any frequency within the frequency bandpass range of the coupled resonant systems. A "weak" instrument may be most likely to happen when the "plate frequency" of the top is too far (or less often too close) to the air volume frequency.

The only thing available to put energy into the "system" is generally the string. The motion of the string that is effective is (ideally) perpendicular to the string, and drives the bridge "up and down." A major source of "lost energy" is any construction detail that allows lengthwise (in the direction of the string) motion of the string across the bridge. Some approaches to bridge design aim at a "slippery bridge" so that the incidental lengthwise motion dissipates very little energy, while others try for a "rocking bridge" that follows this undesired motion with little dissipation. Consensus opinion seems to be that a "stiff bridge" that prevents the motion from occuring at all gives best results. Perfection with any of these methods is exceedingly difficult.

To make the instrument louder, it is necessary that more of the energy stored in the string must be extracted and transferred to the outside air in each cycle. Since there's a limit to how much energy can be put into the string with each pluck (or WHANG) increasing loudness by changing the design features will always reduce sustain, unless some other trick can be used to provide a "bigger whang" such as heavier strings (or stronger picks).

As to the question asked (which I have assumed isn't what you really want to know) any enclosed air volume with a hole in it has a resonant frequency that can be rattled with little loss. You can change the frequency by changing either the air volume, or the sum of the areas of all the holes.

A "smooth" air volume likely will sound better than one that's "fuzzy" on the inside, and the resonance may be "fuzzy" if irregular obstructions are present in the air space. The sound will be "purer" if the container is "fairly rigid" but for common instruments that conflicts a little with the need to transfer vibrations between the inside air and some large part of the outside/exterior surface.

"Squishy things" inside the air volume may upset the resonance since most such things absorb quite a bit of energy, and convert it to "friction heat" that can't be fed back into the sound.

Radical bridge changes may change the frequency of the top plate, by adding a lumped mass that resists going where it should at the same frequency the plate wants, but since all "plate vibrations" are inherently nonlinear the top plate resonance is rather ill defined. It's more likely that unwanted effects for most bridge amendments are due largely to "slippy string" effects unless an unusually heavy bridge amendment is added (or removed).

EVERYTHING about most instruments is a compromise, so concentrating excessively on a single effect, without considering what it does to the rest of the instrument, can produce effects impossible to predict.

"Magic Cures" for an unsatisfactory instrument do not exist - usually.

John