A guitar string is pinned at both ends, so the simplest wave it can hold is one bump — HALF a wavelength — between the pins. Call the vibrating length between those pins $L$, in metres: the wavelength is then $2L$, and with $v = f\lambda$ the lowest note follows: $f_1 = \dfrac{v}{2L}$ — read aloud: f-one equals v over two-L, where $v$ is the speed of waves along the string in m/s and $f_1$ (said f-one) is the lowest frequency it can sound, in hertz. That lowest note is the fundamental, and the subscript 1 marks it as rung one of a ladder.

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: $f_n = n\,f_1$, where $n$ is a plain counting number with no unit: $n = 1$ is the fundamental itself, $n = 2$ the second harmonic, and $f_n$ is that rung's frequency.

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