basic

Standing-Wave Fundamental Frequency on a String Calculator

f₁ = (1/(2L)) · √(T / μ); harmonic n: f_n = n · f₁.

Compute the fundamental frequency f₁ and the first two overtones of a stretched string fixed at both ends from the string length L, tension T (newtons), and linear mass density μ (kg/m): f₁ = (1/(2L)) · √(T/μ). Each higher harmonic is f_n = n · f₁. Defaults model a tuned guitar low-E string.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

m
N
g/m

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

f₁ = (1/(2L)) · √(T/μ); v = √(T/μ).

In depth

Compute the fundamental frequency f₁ and the first two overtones of a stretched string fixed at both ends from the string length L, tension T (newtons), and linear mass density μ (kg/m): f₁ = (1/(2L)) · √(T/μ). Each higher harmonic is f_n = n · f₁. Defaults model a tuned guitar low-E string.