Organ Pipe Frequency Calculator

Work out organ pipe frequency instantly with clear inputs, formula shown and shareable results.

About Organ Pipe Frequency Calculator

An open pipe holds a half wavelength and sounds v/2L; a stopped pipe holds only a quarter wavelength and sounds v/4L, an octave lower for the same length. A closed end forces a displacement node, which suppresses the even harmonics entirely - the reason a stopped organ rank has its distinctive hollow tone.

Formulas

Open pipe

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

Stopped pipe

f(n) = n v / 4L, odd n only

Worked example

With the default values below, Organ Pipe Frequency Calculator returns Fundamental Frequency of 343.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Pipe lengthminimum 0 m: 0.5 m
Speed of sound in the pipeminimum 0 m/s: 343 m/s
Pipe typeone of Open at both ends, Closed at one end (stopped): Open at both ends

Results

Fundamental Frequency: 343.000 Hz
Next Available Mode: 686.000 Hz
Fundamental Wavelength: 1.0000 m
Harmonic Series: All harmonics present (1, 2, 3 ...)

Step by step

1Values used
2Open pipe
3Stopped pipe
4Fundamental Frequency= 343.000 Hz
5Next Available Mode= 686.000 Hz
6Fundamental Wavelength= 1.0000 m
7Harmonic Series= All harmonics present (1, 2, 3 ...)

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 is a stopped pipe an octave lower?

It fits only a quarter of a wavelength instead of a half, so the wavelength is twice as long for the same tube - which halves the frequency.

What about end correction?

Real open ends radiate slightly beyond the tube, adding roughly 0.6 times the radius per open end. This calculator uses the ideal length.