# Open-ended Pan Flute

I made an instrument similar to a pan flute using straws, with the difference in it being an open-open tube as opposed to a traditional pan flute which has an open-closed tube. This page will be investigating the various lengths needed to play different frequencies.

## What is a Pan Flute?

Playing Technique

A pan flute, also known as a panpipe, is an end-blown, open-closed tube musical instrument made up of numerous pipes of gradually increasing length. Pan flutes come in a variety of shapes and sizes, and they've long been popular as folk instruments. Bamboo, giant cane, or reeds are commonly used to make pan flutes.[1]

## Playing Technique

The open-open tube pan flute I made using straws

The pan flute should be placed against the lips with the long pipes on the right and the short ones on the left. Your right hand should support and lightly hold the panpipes at the end of the short pipes, while your left hand should support and lightly grasp the lower half of the longer pipes. Ensure that the pan flute is positioned below the lower lip. It's critical to feel sure the lower lip is actually above the tube while moving the instrument, to avoid needless friction. Now, gently open your mouth, as if smiling, and form a small nozzle, letting out a small amount of air to play a tone.[2]

## How does frequency change with length?

### Calculating the frequency of each straw based on length

Initially, I used the following equation to calculate the frequency:[3]

${\displaystyle f={v \over 2L}}$

v = Speed of sound in air

L = Length of the straw

However, I realized that I had much thinner straws than a normal pan flute, so I adjusted the formula to account for the diameter as follows:

${\displaystyle {\displaystyle f={v \over 2(L+0.6d)}}}$

d = Diameter of straw

### Findings

I found the frequency and length and inversely proportional. The longer the straw, the lower the frequency it produced. The shorter the straw, the higher the frequency it produced, just as the formula was suggesting.

### Why does that happen?

A standing wave is formed when playing an open ended pan flute. That standing wave grows in size as the wind column lengthens. A larger standing wave produces a lower frequency.

### Adjusting lengths to create the wind columns notes

Once I was able to calculate the frequency for my open-ended pan flute, I wanted to adjust the lengths of the straws so that I would be able to play a full scale of wind column notes (C,D,E,F,G,A,B,C). In order to calculate the lengths that I required to achieve that, I used the following formula:[4]

${\displaystyle L=w/2-((0.4)(d))}$

w = Wavelength

d = Diameter of straw

From there, I tried to use audacity to confirm the notes were accurate. However, unfortunately, the instrument is not loud enough for audacity to show an accurate time graph. An example can be seen in figure 4.

Figure 4 - Time graph for C note