What is the formula for an open tube?

For a tube open at both ends, the resonant frequencies are f_n = n × v / (2L), where n = 1, 2, 3, … (all harmonics), v is the speed of sound, and L is the tube length. The fundamental (n = 1) is v / (2L).

What is the formula for a closed tube?

For a tube closed at one end and open at the other, resonant frequencies are f_n = n × v / (4L), where n = 1, 3, 5, … (odd harmonics only). The fundamental is v / (4L), which is half the open-tube fundamental for the same length.

Why does a closed tube produce only odd harmonics?

A closed end forces a displacement node (zero movement) while an open end forces an antinode (maximum movement). Only odd multiples of the quarter-wavelength satisfy both boundary conditions simultaneously, excluding even harmonics.

What speed of sound should I use?

In air at 20 °C the speed is approximately 343 m/s. It increases by about 0.6 m/s per °C. For other gases or liquids, enter the appropriate speed — the tool accepts any positive value in m/s.

Does tube diameter affect the results?

For this ideal model, no — only length matters. In practice, narrow tubes have an end-correction factor (roughly 0.3–0.6 × radius per open end) that slightly lengthens the effective acoustic length. The correction is small for tubes with length much greater than diameter.

How many harmonics does this calculator show?

It displays the first ten resonant modes. For open tubes that is harmonics 1–10; for closed tubes it is odd harmonics 1, 3, 5 … 19.

Resonant Frequency of a Tube

Enter tube length and tube type to instantly calculate all harmonic resonant frequencies and their wavelengths.

Tube Parameters

Tube Length

Tube Type

Open Both ends open Closed One end closed

Speed of Sound (m/s)

Resonant Modes

Set the tube parameters and click Calculate Resonant Frequencies.

Fundamental

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Formula

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Harmonic	Frequency	Wavelength

Standing Wave Diagram — First Three Modes

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Summary

This calculator finds the resonant (natural) frequencies of cylindrical tubes modeled as acoustic resonators. For an open tube (open at both ends), all harmonics are present and the fundamental frequency is v / (2L). For a closed tube (closed at one end, open at the other), only odd harmonics appear and the fundamental is v / (4L). Results include frequency, wavelength, and harmonic number for the first ten modes.

How it works

Enter the tube length in meters, centimeters, or millimeters.
Select the tube type: Open (both ends open) or Closed (one end closed).
Optionally adjust the speed of sound — defaults to 343 m/s (air at 20 °C).
The calculator applies f_n = n·v / (2L) for open tubes and f_n = n·v / (4L) for closed tubes (odd n only).
Results table lists the harmonic number, frequency, and corresponding wavelength for the first ten resonant modes.
Click any row to highlight it; use the Copy button to export results as plain text.

Use cases

Design organ pipes and wind instruments tuned to specific pitches.
Determine resonance peaks in HVAC ducts and exhaust pipes.
Analyze standing waves in laboratory tube experiments.
Verify acoustic resonance in muffler and silencer design.
Support physics coursework on standing waves and harmonics.
Calculate fundamental frequency of a PVC pipe for DIY instrument projects.
Estimate resonance in barrel-shaped enclosures and speaker ports.
Predict resonant modes in industrial piping before assembly.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu