Since it's is too generic saying "I want to play an E", we must specify also the octave. Each tube will produce a note a semitone higher than the previous one and a semitone lower than the next one. I'm going to make a full octave pan flute, so I need 13 tubes: C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B and C again. Now we need to determine which notes we want to produce, and their frequencies.
Here is the meaning of various symbols: - L is the length of the tube - v is the speed of sound - f is the frequency Fine. The formula we need is the one in the first pic. So we can "stole" their results to serve our scopes. Luckily, some physician (well, actually a lot of physician) already studied this matter creating and developing a branch of physics called acoustic. Now we need to find a precise relation between tube length and note pitch. Pretty simple, uh? No math, no strange formulas. The inner diameter of the tube influence the speed of blow needed to make the sound audible: smaller diameter means less blow, greater diameter means more blow. The length of the tube influence the pitch: longer tubes produce lower notes, shorter tubes produce higher notes. Each tube have a different length but, usually, the same diameter of all other tubes. I'm here for this! A pan flute is a mere group of tubes with a closed end (called closed cylinder, even if one end is open). OK, if you're reading those words you want to know more. As I've aforementioned, you can skip this passage if you don't want (or need) to understand the physics beyond a pan flute.
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