Guitar String Harmonics Simulator (2D)

String

Scale length L 0.65 m

Tension T 70 N

Linear density μ 1.0 g/m

Harmonic / Fret

Touch / fret position open string

Fundamental (n=1) ringing.

Live Readout

Wave speed v

0 m/s

Fundamental f₁

0 Hz

Frequency f_n

0 Hz

Wavelength λ_n

0 m

How it works

A stretched string of length L, tension T and linear mass density μ supports transverse waves that travel at speed v = √(T/μ). Only wavelengths that fit an integer number of half-waves between the two fixed ends — the nut and the bridge — survive as standing waves, giving wavelength λ_n = 2L/n and frequency f_n = n·v/(2L) for harmonic number n = 1, 2, 3…

Each harmonic n has n+1 nodes (points that never move, including the two ends) and n antinodes (points of maximum swing) evenly spaced along the string. Touching the string lightly — without pressing it to a fret — exactly at a node of harmonic n damps the fundamental and every harmonic that does not share that node, letting only harmonic n and its multiples ring: the "natural harmonic" or flageolet technique guitarists use for a bell-like tone and for tuning strings against each other.

Raising the tension or shortening the string raises every frequency (v grows with √T, and f_n scales as 1/L), which is exactly how tuning pegs and fretting a string work on a real guitar.

Node — string motionless Antinode — maximum swing Touch / fret point