Editing Pan flute (section)

=== Acoustics ===
The pan flute is an [[end-blown flute]].  Sound is produced by the vibration of an air-stream blowing across an open hole at the end of a resonating tube.  The length of the tube determines the fundamental frequency. An overblown harmonic register is near a 12th above the fundamental in cylindrical tubes, but can approach an octave jump (8th) if a decreasing taper is used.{{Cn|date=February 2021}}

According to the Fundamental Principle for pan flutes, the frequency and the length of the tube are inversely proportional. Every time the pitch goes up one [[octave]], the frequency doubles. Because there are 12 notes in a [[chromatic scale]] or a full octave, every half-step in a chromatic scale is multiplied by the 12th root of 2 to get the note next to it. By this, it is possible to calculate the length of any pipe, given that one knows the length of any one pipe. The formula for calculating the length of a pan flute pipe is '''L&nbsp;=&nbsp;(c / f)&nbsp;/&nbsp;4''' (the "theoretical length" L equals the [[speed of sound]] c = 343&nbsp;m/s, divided by the desired frequency in [[hertz]] f, that quantity divided by 4; this simplifies and rearranges to: Length of pipe (in [[centimeters]]) × [[Frequency]] (in [[hertz]]) = 8575). Because of a property of compression within the tube, the length must be a little shorter to correct flat pitch. The extra length is helpful for a maker, who can use a cork or plug at the bottom to adjust the pitch. Some instruments use wax or pellets to tune the fundamental pitch of each tube. A tube that has a diameter 1/10 of its length yields a typical tone colour (see [[Timbre]]). An inner diameter range between 1/7 and 1/14 of the length L is acceptable. A narrow tube will sound "reedy", while a wide one will sound "flutey". A more exact method is to 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. Only tiny adjustments will be needed then to adjust fundamental pitch for air density and temperature.<ref>{{cite web |url=http://www.sarahtulga.com/panpipes.htm|title=Panpipes|last=Tulga|first=Sarah}}</ref><ref>{{cite book|last=Olson|first=Harry F|title=Music, Physics, and Engineering|year=1967|publisher=Courier Corporation |isbn=9780486217697 |url=https://archive.org/details/musicphysicsengi0000olso|url-access=registration}}</ref><ref>{{cite book|last=Price|first=Lew Paxton|title=Secrets of the Flute}}</ref><ref>{{cite book|last=Benade|first=Arthur H|title=Horns, Strings and Harmony|year=1960 |publisher=Garden City, N.Y., Anchor Books |url=https://archive.org/details/hornsstringsharm00bena|url-access=registration}}</ref>