Standing Wave and Harmonics Calculator

What this tool does

A string fixed at both ends, or a pipe open at both ends, fits a whole number of half-wavelengths, so the harmonics come out as simple multiples of the fundamental — which is what makes them sound musical. A pipe closed at one end fits only odd quarter-wavelengths and sounds an octave lower for the same length, which is the fourth result.

Formula

f = n × v ÷ (2L) (string or open pipe)

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.