It is determined by the fret scale, and the intonation depends on correct placement of the bridge relative to the fret scale.
The afterlength of the string is the vibrating part between the bridge and the tailpiece. It is is colored red here.
Here are two tailpieces each yielding a different afterlength:
With the Waverly, left above, it is much shorter than with the No-Knot at right.
Does this matter? In violins, yes, but with banjos, I sure don't think so.
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