A guitar string is pinned at both ends, so the simplest wave it can hold is one bump — HALF a wavelength — between the pins. Wavelength $2L$, and with $v = f\lambda$ the lowest note follows: $f_1 = \dfrac{v}{2L}$ — read aloud: f-one equals v over two-L ($f_1$ is said f-one, and it is called the fundamental).

The ear-test you can run at any fretboard: halve the length and the pitch DOUBLES — the twelfth fret sounds the octave. Above the fundamental climb the harmonics, the fundamental's multiplication table: $f_n = n\,f_1$.

And what sets $v$ itself? Tension and heft: $v = \sqrt{\dfrac{F}{\mu}}$ — v equals root F over mu, where $\mu$ (said mew) is the string's mass per metre. Tighter runs faster, heavier runs slower — exactly why the tuning peg works and why the low strings are wound fat.