Standing Wave Calculator
Find allowed harmonics for two matching boundary conditions.
Find harmonics between matching boundaries
A string fixed at both ends and a pipe open at both ends support integer harmonics whose wavelength is twice the length divided by harmonic number. This calculator combines that wavelength with wave speed to report frequency. It is useful for checking string modes, ideal open-pipe resonances, and classroom standing-wave diagrams with matching boundary conditions at both ends.
For length 1.2 meters, wave speed 240 meters per second, and third harmonic, wavelength is 0.8 meter and frequency is 300 hertz. The fundamental at the same length and speed would be 100 hertz. Harmonic number must be a positive integer because each allowed mode fits an exact number of half wavelengths into the length.
Choose the boundary model before using the result
A pipe closed at one end follows odd quarter-wave modes and is not represented by this equation. Real strings have stiffness and end corrections, while sound speed and tension can vary with conditions. Calculations take place in your browser. Select a wave speed appropriate to the medium, and use measured effective length when supports or openings shift the nodes.
Frequently Asked Questions
Which systems use this harmonic equation?
It fits strings fixed at both ends and ideal pipes open at both ends because both have matching end conditions.
Can harmonic number be a decimal?
No. The supported modes use positive integer harmonic numbers for these matching boundaries.
Does this model a pipe closed at one end?
No. A closed-open pipe supports odd quarter-wave modes and needs a different expression.
Browse the full set of free, private, in-browser tools.