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Standing Wave Harmonics Calculator

Work out standing wave harmonics instantly with clear inputs, formula shown and shareable results.

About Standing Wave Harmonics Calculator

A string fixed at both ends supports standing waves whose wavelengths fit a whole number of half-waves into its length, so f(n) = n.v/(2L). A 0.65 m string carrying waves at 200 m/s has a 153.8 Hz fundamental, and its third harmonic sits at 461.5 Hz with four nodes. The harmonic series is exactly integer, which is why plucked strings sound musical.

Formulas

Harmonic frequencies

f(n) = n v / (2L)

Mode wavelength

lambda(n) = 2L / n

Worked example

With the default values below, Standing Wave Harmonics Calculator returns Frequency Of That Harmonic of 461.539. Change any input above and every figure here is recalculated in your browser.

Inputs used

Length of the mediumminimum 0 m
0.65 m
Wave speedminimum 0 m/s
200 m/s
Harmonic numberminimum 1
3

Results

Frequency Of That Harmonic
461.539 Hz
Fundamental Frequency
153.846 Hz
Wavelength Of That Mode
0.43333 m
Number Of Nodes Including The Ends
4

Step by step

  1. 1Values used
  2. 2Harmonic frequencies
  3. 3Mode wavelength
  4. 4Frequency Of That Harmonic= 461.539 Hz
  5. 5Fundamental Frequency= 153.846 Hz
  6. 6Wavelength Of That Mode= 0.43333 m
  7. 7Number Of Nodes Including The Ends= 4

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 5 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 the harmonics whole-number multiples?

Because both ends must be nodes, so only whole numbers of half-wavelengths fit. Drums and bells have two-dimensional modes and are not so simple.

How do I raise the pitch of a string?

Shorten it, tighten it or use a lighter string. Frequency goes inversely with length and with the square root of tension.

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