I'm working in OpenSCAD to draw up a 3D model of a pan flute that I could print out using a 3D printer and (with any luck!) play right there on the spot. I've looked up some of the formulas for determining the pitch of a open ended tube but I have some questions...
Wikipedia says that the formula for calculating the length L of a pipe with a frequency F is
L = (S/F) / 4
where S is the speed of sound.
It goes on to say:
"Because of a property of compression within the tube, the length must be a little shorter to correct flat pitch"
and also that:
"If you are a "perfectionist", multiply the bore diameter by 0.82 and subtract this value from the tube length. This compensates for internal compression slowing frequency and the lips partially covering the voicing."
I'm wondering where this 0.82 comes from, and across which values it will be relevant. Is that 0.82 going to give the 100% correct compensation for exactly one length? Or maybe one length-to-diameter ratio? If that's the case I could increase the diameter of the longer tubes, keeping the length to diameter ratio constant, and if not, I can keep the diameter constant for all pipes.
Any help would be greatly appreciated!