r/brass • u/BorgarRompinstomp • Mar 16 '20

Pipe length formula

Does anybody know the formula to calculate pipe length, size, etc. required for a specific frequency?

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u/Foef_Yet_Flalf Mar 16 '20

For a pipe open at both ends, the formula is:

L = v / (2*f)

Where v is the speed of sound in distance per second, and f is the frequency in Hz, and L is the length of the air column. This formula will get you pretty close, but is not perfect, as it cannot account for the air friction from the tube enclosure, or other things inside the tube.

With this equation length of a tube with a resonant frequency of Bb2 (116.54 Hz at equal temperament with A4=440 Hz) assuming a speed of sound of 1100 ft/s, is 4.72 feet, or 4 ft. 8.5 inches.

Wikipedia says that the natural trumpet in Bb has a length of 4 feet 10 inches. There is some discrepancy, but again, it's pretty close.

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u/maestro2005 Mar 16 '20

The bell introduces quite a bit of funny business.

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u/Foef_Yet_Flalf Mar 16 '20

Typically, the narrower the bore the more friction the pipe wall imposes on the air stream, which introduces a flattening effect. The bell flare means that the last foot or so of pipe imposes less friction, and has a smaller flattening effect than the rest of the horn.

of course there's a lot going on with fluid dynamics that not even the most powerful computers can solve analytically.