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String Vibration Frequency Calculator

Work out string vibration frequency instantly with clear inputs, formula shown and shareable results.

About String Vibration Frequency Calculator

Waves travel along a string at sqrt(T/mu), so the fundamental is (1/2L)sqrt(T/mu). A 648 mm string at 70 N with 0.4 g/m gives 324 Hz, close to E4. Because tension appears under a square root, raising pitch by an octave needs four times the tension - which is why thicker strings are used instead.

Formulas

Wave speed on a string

v = sqrt(T / mu)

Fundamental (Mersenne's law)

f1 = (1 / 2L) sqrt(T / mu)

Worked example

With the default values below, String Vibration Frequency Calculator returns Fundamental Frequency of 322.786. Change any input above and every figure here is recalculated in your browser.

Inputs used

Vibrating lengthminimum 0 m
0.648 m
String tensionminimum 0 N
70 N
Mass per unit lengthminimum 0 kg/m
0.0004 kg/m

Results

Fundamental Frequency
322.786 Hz
Wave Speed On The String
418.330 m/s
Second Harmonic
645.571 Hz
Fundamental Wavelength
1.2960 m

Step by step

  1. 1Values used
  2. 2Wave speed on a string
  3. 3Fundamental (Mersenne's law)
  4. 4Fundamental Frequency= 322.786 Hz
  5. 5Wave Speed On The String= 418.330 m/s
  6. 6Second Harmonic= 645.571 Hz
  7. 7Fundamental Wavelength= 1.2960 m

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why are bass strings thick or wound?

To raise mu without raising stiffness. A heavier string vibrates more slowly at playable tension, which is what wound strings achieve compactly.

How much does tension change pitch?

Frequency scales with the square root, so a 2% tension change shifts pitch by about 1% - roughly 17 cents.

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