Standing Wave Tube Frequency Calculator
A column of air in a tube resonates at frequencies set by its length and which ends are open or closed. Open-open tubes sound all harmonics with a fundamental of c divided by twice the length; closed-open tubes sound only odd harmonics with a fundamental one octave lower. This calculator returns the first few resonances for both configurations from the tube length and the speed of sound. It is the standard tool for flute and organ-pipe work, resonance-tube physics experiments, and duct acoustics. The speed of sound is editable so you can match your air temperature; the result uses the ideal length without end correction.
Air-column resonance formulas
Open-open: f(n) = n * c / (2 * L), n = 1, 2, 3, ...
Closed-open: f(n) = (2n - 1) * c / (4 * L), n = 1, 2, 3, ...
c = speed of sound (m/s), L = tube length (m)
The open-open series contains every harmonic; the closed-open series contains only odd harmonics and has a fundamental one octave below the open-open tube of the same length.
Worked example
A 0.5 m tube at c = 343 m/s: open-open fundamental = 343 / (2 * 0.5) = 343 Hz, with harmonics at 686, 1,029, 1,372 Hz. Closed-open fundamental = 343 / (4 * 0.5) = 171.50 Hz, with odd harmonics at 514.50, 857.50 Hz.
Standing wave tube: frequently asked questions
What is a standing wave in a tube?
A tube of air resonates at frequencies where a standing wave fits between its ends. The boundary conditions depend on whether each end is open (a pressure node, displacement antinode) or closed (a pressure antinode, displacement node). Wind instruments, organ pipes, and resonance-tube experiments all rely on these resonances.
What are the formulas for open and closed tubes?
An open-open tube (both ends open) resonates at f = n times c divided by (2 times L) for n = 1, 2, 3, and so on, giving all harmonics. A closed-open tube (one end closed) resonates at f = (2n minus 1) times c divided by (4 times L), giving only odd harmonics. Here c is the speed of sound and L is the tube length.
Why does a closed tube sound an octave lower?
A closed-open tube of the same length has a fundamental of c divided by 4L, exactly half the c divided by 2L fundamental of an open-open tube. That is why a stopped organ pipe sounds roughly an octave below an open pipe of the same length and produces only odd harmonics.
Should I add an end correction?
Real open ends radiate slightly beyond the physical tube, so the effective length is a little longer than the measured length, lowering the true frequencies. A common end correction is about 0.6 times the tube radius per open end. This calculator uses the ideal length; add an end correction for precise instrument work.
Official sources
- U.S. National Institute of Standards and Technology: nist.gov (speed of sound reference values).
- NIST Reference on Constants, Units, and Uncertainty: SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.