How does string length affect the pitch produced by a violin or guitar?

In the context of musical sound, the relationship between string length and pitch is defined by Mersenne’s laws. These laws state that the fundamental frequency of a stretched string is inversely proportional to its length, provided that the tension and the mass per unit length remain constant.1

In practical terms, this means that as the length of a vibrating string is shortened, the pitch produced becomes higher. Conversely, increasing the length of the string results in a lower pitch. This principle is fundamental to the operation of string instruments like the violin and guitar, where players change the vibrating length of the strings by pressing them against a fingerboard or frets to produce different notes.12