basic

Vibrating-String Fundamental Frequency from Tension, Length, and Linear Density Calculator

f₁ = (1/2L) · √(T/μ).

Compute the fundamental frequency f₁ of a stretched string of length L, tension T, and mass-per-length μ. f₁ = (1/2L) · √(T/μ). Also reports the wave speed v = √(T/μ) and the first three overtones (f₂ = 2f₁, f₃ = 3f₁, f₄ = 4f₁). Higher tension and lower mass-per-length give a higher pitch.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

N
m
kg/m

Results

Enter values and click Calculate to see results.
Was this helpful?

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 of a stretched string of length L, tension T, and mass-per-length μ. f₁ = (1/2L) · √(T/μ). Also reports the wave speed v = √(T/μ) and the first three overtones (f₂ = 2f₁, f₃ = 3f₁, f₄ = 4f₁). Higher tension and lower mass-per-length give a higher pitch.