Pan pipes

The pan flutes (also known as panpipes or syrinx) are a group of musical instruments based on the principle of the closed tube, consisting of multiple pipes of gradually increasing length (and occasionally girth). Multiple varieties of panflutes have long been popular as folk instruments. The pipes are typically made from bamboo, giant cane, or local reeds. Other materials include wood, plastic, metal and ivory.

The pan flute is named after Pan, the Greek god of nature and shepherds often depicted with such an instrument.

The pan flute's tubes are stopped at one end, at which the standing wave is reflected giving a note an octave lower than that produced by an open pipe of equal length. In the traditional South American style, pipes are fine-tuned to correct pitch by placing small pebbles or dry corn kernels into the bottom of the pipes. Contemporary makers of curved Romanian-style panpipes use wax (commonly beeswax) to tune new instruments. Special tools are used to place or remove the wax. Corks and rubber stoppers are also used, and are easier to quickly tune pipes.

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.

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 = (c / f) / 4 (the "theoretical length" L equals the speed of sound c = 343 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". 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. Only tiny adjustments will be needed then to adjust fundamental pitch for air density and temperature.

...
Wikipedia