RESONANCE FREQUENCIES
A quantitative approach makes sense regarding resonance frequencies of air volume, top and back of a string instrument like a guitar, violin, ukulele or any other string instrument. The parameters are not independent which makes control of the values of these frequencies so challenging. The values and ratios of resonance frequencies are actually very important to make an instrument stand out above the average. Resonance frequencies can be measured and modified during the building process which leads to better instruments and more consistency in quality. One approach is to aim for a peak resonance frequency of the top which is approximately the double of the air resonance frequency and a peak frequency of the back approximately one or two semi tones under or above the resonance frequency of the top. Coupling between the various resonance frequencies enriches the quality of the tone of the instrument. A lot can be learned from violin builders and builders of classical guitars. The old masters in violin building had a good understanding of the importance of the interaction between back and top for several centuries. A book by R H Siminoff, "The Art of Tap Tuning" is a good start to learn more about the subject.
For a high quality classical guitar the body air resonance is usually one octave and a semi-tone lower than the tap-tone of the top. The air resonance frequency tells a lot about the character of an instrument and is normally in the range E# to A. It tells whether it has a more dark or a brighter tone at the lower end of the spectrum.
Visualisation of ring mode of Favino Manouche
guitar top during construction