A Tuneable Pan Flute made from the 20mm PVC conduit available in Australia.

Including calculation of the tube lengths


My granddaughter had to make a simple musical instrument for a school project and I was asked to help.
Pan Flute construction consists of basically cutting some tube into lengths, blocking the ends and fixing the tubes in line.
At Masters Hardware I bought a 4m length of Tripac RCW20 20mm communications conduit (Id. 1.6cm). A bottle of clear PVC Pipe Cement ( later found to lack strength and was unsuitable
) and a Crescent rotary conduit cutter (see picture below). The first two items totalled about $7 the cutter around $25 but it was worth the price as it gave a clean neat square cut and seemed safe and easy for my granddaughter to use. I wrote down the formula to work out the lengths required and the frequencies of 10 notes of the C major scale starting from middle C on up, transferred some pipe cement into an old nail polish bottle (the brush in the original bottle is unwieldy for small jobs), found some 5c coins to close the ends of the tubes and handed over the kit and my granddaughter took it from there. The flute was finished off by tying the tubes together with some wool and then gluing them together.


With the project handed in I pondered improvements. It would be better without the use of coins and if it was tuneable. I think I have the solution see below.

The Internet revealed for a speed of sound S the length L of a closed tube resonates at frequency F when

L =  (S / 4F) - E     where E is known as an end correction.

The end correction for an isolated pipe is 0.6133r  where r is the radius (E = 0.49 for 1.6cm). Unfortunately a blown pipe is not isolated and ones face make a large difference. Wikipedia gives the end correction for pan pipes as .82 d  where d is the diameter (E = 1.31 for 1.6cm).  I wondered what the end correction for my face and blowing technique was.


The above equation can be arranged as   S = 4F(L + E)
 
Take two tubes of different lengths La  Lb  and find the blown frequencys  Fa  Fb

Sa = 4Fa(La + E)   Sb = 4Fb(Lb + E)

By assuming that the speed of sound  was the same for the two tests.

4Fa(La + E) =  4Fb(Lb +E))

E = (FaLa  -  FbLb)/(Fb - Fa)

Two tubes of length 28.25cm and 13.57cm   produced tones of 293.22 and 586.23 giving E = 1.12

Just for the fun of it now we know E we can work out the speed of sound in the tube.
It came to 34494cm/second which is the speed in free air (from tables) at about 2C  above the ambient that was 19.2C.
I attempted to take the temperature inside a tube while blowing notes and 2C above ambient seems reasonable.
To calculate the pan flute lengths at an ambient of 20C I decided to use a speed of sound of 34500cm/sec corresponding to a pipe temperature of about 22C.


AP Tuner ( free software ) was used to determine the frequency see www.aptuner.com
Multiple notes were sounded and the mid-point frequency of the notes averaged.

The vertical divisions shown are cents (100 cents per semitone) and the frequency of this test varied
from -13 to +5 corresponding to 583 to 589





A tuneable conduit pan flute.


I discovered that the end of the tubes could be blocked successfully by a "Tack" type product - Blu-Tack, U-Tack etc..
The inside lengths could be marked on a dowel rod which sets the correct depth and the "Tack" pressed down onto it.
The "Tube Length" in the table below allows about 2.0 cm extra length to accommodate the "Tack" stopper.


Speed of sound S=34500 cm/second   End correction E=1.12 cm  L =  (S / 4F) - E
NoteFrequencyInside Length cmTube Length cm
C4261.6331.8533.8
D4293.6628.2530.2
E4329.6325.0427.0
F4349.2323.5825.6
G4392.0020.8822.9
A5440.0018.4820.5
B5493.8816.3418.4
C5523.2515.3617.4
D5587.3313.5715.6
E5659.2611.9614.0
The scale can be converted to G major by changing F4 to F4#  369.99  inside length 22.19 cm



























A 90cm length of 16mm pine dowel, straight and smooth with good square ends was purchased from Bunnings and cut in half. 
Bunnings only had grey electrical conduit but I believe it has the same dimensions as the white communications type from Masters.
With either  type of tube it may be necessary to smooth the dowel with sandpaper for an easy sliding fit in the tube.
The required lengths were marked onto the dowel from the best end.
The dowel was inserted into the tube to the correct depth and a ball of "Tack" about the diameter of the tube was inserted and pressed against the end of the dowel.
The "Tack" must make a perfect seal for the tube to resonate and it needs to be worked in enough against the dowel to form a good square bottom.
When the outside of the tube was placed near a light I could check the seal.
The seal on the right below needs more work.

   

















The sharp outside top rim of the tubes can be smoothed off to proct ones lips.  I found a "diamond" nail file worked well when followed by a nail buffer.



To see if the rim shape made the pipe harder or easier to sound I made a two E5 pipes one rounded and one sharp.
I found no difference in how easy they were to sound or in the sound produced.



Keep the tuning rod as the long term stability of the "Tack" is not known.




A tuned pipe.
How it is blown makes a huge difference.






A demonstration set of pipes.


Pipe jointing cement was used to join the pipes but it lacked strength so
they were bound in cotton cooking string that was then soaked in super glue.
By using a drop of super glue to fix the first loop and the last one a neat job without crossovers or knots can be produced.