I have been trying to create a xylophone out of copper pipes for a school project and have been running into a few problems with calculating the length of each bar. I have been using this paper as reference, specifically equation (1). I have cut two pipes so far with lengths of 0.884m and 0.585m which played the notes B3 and A♭6 respectivly, which is far from the expected E2 and G♭3. For reference, my pipes have an inner radius of 0.25 in and an outer radius of 0.3125 in.
Even when I tried "reverse calculating" the speed of sound in the bar using (1) with both sets of data, I got answers both different from the expected 3700 m/s and from each other. Does anybody have any idea why this could be, either an error on my part or in my calculations? Is there another equation I should be using or is it more likly I am just making some silly error?
For reference, here are my calculations for the 0.884m bar:
K = 1/2 sqrt(0.25^2 + 0.3125^2) = 0.2 in = 0.0048 m
f = (pi * v * K * 3.011^2) / (8 * L^2) = (pi * 3700 m/s * .0048 m * 3.011^2) / (8 * (0.884 m)^2) = 80.9 Hz
This is around (a bit lower than) the frequency of E2, but when tested the tuner registers B3.
After some more tinkering around and reading through some comments, I am more lost than ever. I tried mounting the bars this time using rubber foam weather seal but the pitch was being registered even more spastic from the tuner. I have attached a video here, which hopefully can be of use.