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The f-hole is a cut in the side of an acoustic stringed instrument, usually in the violin or guitar family. It is shaped like a cursive lowercase f or long s.

The object of the f-hole, like any soundhole, is to provide some escape for the sound -- the hollow body of the instrument amplifies the sound -- and also to affect the tone of the sound, as well as the aesthetic effect.

The shape and position of the hole determine the tonal qualities of the instrument, partly through their location (and possibly the harmonics created) and through the bracing of the instrument.

The f-hole is one way to tell a Stradivarius violin from a copy; the holes were cut and placed in a certain way.
Archtop guitars also have f-holes instead of the normal round soundhole of an acoustic guitar. This may be due to the design and bracing of the guitar.

Rickenbacker acoustic-electric guitars are noted for having f-holes. In this case, it seems to be more of a style choice than a design necessity.

with help from http://members.aol.com/loenviolin/straddoc.htm

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