Raphi Giangiulio's Homemade Pipe Organ

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Calculating the Internal Length of a Pipe

The internal length of a pipe is defined in the image to the right. The three main factors in calculating the internal length are the frequency of the note, whether it is a stopped or open pipe and the size of the pipe. The frequency determines the wavelength of the soundwave:

λ =13543
f
  • λ is the wavelength in inches
  • f is the frequency in Hz
  • 13543 is the approximate speed of sound in inches per second

An open pipe will contain one half of a wavelength and a stopped pipe will contain one fourth of a wavelength:

For an open pipe:IL =λ
2

For a stopped pipe:IL =λ
4

The last thing to consider is a correction factor due to the effect of the air at the end of the pipe. There is a rule of thumb I read about on the following webiste that has shown to be fairly accurate at predicting the internal length. The rule states that you should subtract from the theoretical length two pipe widths for an open pipe and one pipe width for a stopped pipe. Adding in the correction factor and simplifying the expressions gives the following:

For an open pipe:IL =6772 - 2 * IW
f

For a stopped pipe:IL =3386 - IW
f
  • IL is the internal length in inches
  • f is the frequency in Hz
  • IW is the internal width in inches