Why Are Violin Sound Holes Shaped Like an F?

The two f-holes in a violin's top plate are first of all openings through which the enclosed air interacts with the surrounding air; they are not merely decoration. String vibration passes through the bridge into the body, while the top, back and enclosed air move together. Near the instrument's low air resonance, the sound holes are an important route by which sound is radiated.

The decisive feature is not simply the open area, but the edge. Research by MIT acousticians working with violin makers found that airflow around a sound hole is concentrated mainly near its perimeter. As the round holes of earlier instruments developed through C-shaped openings into slender f-holes, the perimeter increased relative to the area, improving the efficiency of radiation from the air resonance. An f-hole provides a long active edge without removing an equally large area of spruce, balancing acoustic conductance with the plate's structure. Measurements of hundreds of Cremonese instruments linked longer f-holes with greater air-resonance power, but the gradual change could have accumulated through small craft variations followed by selection. It does not show that one maker suddenly invented a perfect design.

When listening, there is no need to hunt for an isolated “f-hole timbre”. The openings chiefly affect the efficiency of a low-frequency air resonance, while brightness, response and projection also depend on arching, plate thickness, wood, bridge and playing. Listen instead to the whole instrument: whether the lower register has support and whether the sound continues to open as the player moves from soft to strong. The f-hole matters because it is a mature connection between limited material, moving air and acoustic efficiency, not because it is a mysterious emblem.

https://news.mit.edu/2015/violin-acoustic-power-0210
https://pmc.ncbi.nlm.nih.gov/articles/PMC4353046/