Musical Instrument Project: Frequencies Aren't Right?

[tintinnie]

My requirement for this project was to build an instrument that can produce all the notes in a C scale. The accuracy of the notes is to be judged through Frequency (Hertz). I decided to build an instrument whose design is comprised of eight electrical conduit tubes (metal) that are about 1.5'' inches in diameter. I strike them with a mallet to

Comments

[jewtemplar]

The note that a given pipe sounds is the fundamental, so n=1 for all 8 pipes (i.e. your last C should be 33 cm, assuming the other calculations are right

[tintinnie]

Oh! OK, thank you! That makes a lot more sense-- I was confused as to why I kept coming up with the same number for the last C. 33 cm fits the pattern. And I'm glad the rounding didn't matter too much.

By thin, do you mean like... The size of a flute or a clarinet, perhaps? I guess I made a mistake by buying such a large pipe, but I was worried it wouldn't amplify enough if I used a smaller tube. Is there a good method for amplifying a smaller tube?

If I'm trying to compensate for this end effect, is this the kind of formula I'm looking for? I had trouble finding a formula for "effective length" in regards to a cylindrical tube, and I don't quite understand it myself yet.

I did try and see if the pitch varies depending on the area of the pipe I struck, but it didn't make any audible difference.

Thanks for the detailed comment and all the help!

[jewtemplar]

By thin I mean the diameter of the air inside the pipe, in this case around 1.5." You are right that bigger tubes, with more moving air, will be louder, so I think you should try and compensate for the problem experimentally.

What I would do is to find out what frequencies your tubes are producing. If you have a (reasonably in tune) piano or keyboard, for instance, you can find out between which two piano notes the tube sounds fall and get a sense of the frequency that way using a table of pitches vs. frequencies like http://peabody.sapp.org/class/st2/lab/notehz/ . Using the experimental frequencies you find, you can then solve for the effective length of your pipes. For instance, if a pipe had a frequency of x, the effective length of the pipe would be v/(2x). Then plot the difference between the effective length of the pipe versus the actual length, and see how this deviation varies with (real) pipe length. If that didn't make sense, let me know.

[tintinnie]

Ah, OK, I see. I went and got a tuner, and I unfortunately discovered that I have a G sharp (below middle C), C, E, F sharp, D where I ought to have a C, D, E, F, G. So really, they are very, very flat.

With that being said, I do have a chart of frequencies that someone gave me at my PhysicsForums post. So, just to make sure I understand... If, taking my C pipe for example, I know it's producing the frequency of a G sharp (207.65 Hz), then would I take 207.65 and plug it in for 'x' in the equation v/(2x) to solve for the length that the pipe really should be?

Thanks again for all your great help.

[tintinnie]

Sorry, I'm a little confused!

I was under the impression that the equation I used was for the frequency of a sound produced by an open-ended pipe. This is what I thought: if I'm hearing the sound, it must be traveling through the air-- therefore, the speed of sound through air, and not the speed of sound through the tube (as if I was pressing my ear to the metal). So the equation itself must be fine, mustn't it?

If I'm wrong, then would I have to account for the speed of sound through the metal and through air?

[__k_y_l_e__]

Yeah, ignore me. I was thinking of sound produced by strings when I wrote that.

[tintinnie]

No worries. :) I was just making sure, but thanks for the help anyways!