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Open Pipe Resonance Calculator

Enter the pipe length, harmonic and speed of sound to get the frequency.

Result

1,029.00 Hz
0.33 m

How it is calculated

For a pipe open at both ends, f = n × v / (2L). Here n is the harmonic number (1 is the fundamental), v the speed of sound in m/s and L the pipe length in metres. The wavelength shown is λ = v / f, in metres.

If the speed is left empty the tool uses 343 m/s, and if the harmonic is empty it uses 1. Length and speed must be above zero and the harmonic must be at least 1; the tool does not insist on a whole number, so 2.5 is calculated, but only whole numbers match real resonances. The formula ignores end correction, which makes a real pipe sound slightly lower than predicted, and the speed of sound changes with temperature and gas.

Worked example

An open pipe is 0.5 m long, the speed of sound is 343 m/s and we want the third harmonic. f = 3 × 343 / (2 × 0.5) = 1029 / 1 = 1,029.00 Hz. The wavelength is 343 / 1029 = 0.33 m, which is two thirds of the pipe length and equals 2L / 3, as expected for the third harmonic.

Try this example →

Common mistakes

  • Entering the length in centimetres: the formula is in metres, and 50 instead of 0.5 gives a frequency 100 times too low.
  • Using the formula for a pipe closed at one end: that pipe has only odd harmonics and a fundamental of v / (4L), half the frequency of an open pipe of the same length.
  • Leaving the speed at 343 m/s for a hot room or a gas other than air: the pitch shifts with temperature, so a warm hall raises the frequencies.
  • Expecting an exact match to a real instrument: end correction at the open ends lowers real pitch slightly, so the computed value is a little high.

About this calculator

An open pipe (open at both ends) resonates when it fits a whole number of half-wavelengths, giving harmonic frequencies f = n·v/(2L), where n = 1, 2, 3... is the harmonic number, v is the speed of sound (≈343 m/s in air at 20°C), and L is the pipe length. Unlike a closed pipe, which only supports odd harmonics, an open pipe supports every integer harmonic, which is why its tone sounds fuller and brighter.

Musical-instrument makers and acousticians use this relationship to design and tune open flue pipes in organs, flutes, and open-ended resonance tubes, since it directly determines the pitch produced for a given pipe length and lets a builder work backward from a target note to the required length.

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