String Vibration Calculator — Formule
## Vibrating String
A string fixed at both ends supports standing waves whose frequencies depend on string length, tension, and mass per unit length.
### Formula
**f_n = (n / 2L) * sqrt(T / mu)**
where T is tension, mu is linear mass density (kg/m), L is string length, and n is the harmonic number.
A string fixed at both ends supports standing waves whose frequencies depend on string length, tension, and mass per unit length.
### Formula
**f_n = (n / 2L) * sqrt(T / mu)**
where T is tension, mu is linear mass density (kg/m), L is string length, and n is the harmonic number.
Exemple Résolu
A guitar string: L = 0.65 m, T = 73 N, mu = 0.001 kg/m, fundamental.
- v = sqrt(T / mu) = sqrt(73 / 0.001) = sqrt(73000) = 270.2 m/s
- f = (1 / (2 * 0.65)) * 270.2
- f = 0.769 * 270.2
- f = 207.8 Hz