WIND CHIMES

[Andrew Douglas Delano]

Hello,

I'm trying to make some wind chimes from some aluminum tubing. Does
anyone know of equations which relate the tube parameters (ie. length,
OD, ID) to the note at which the tube will sound?

Thanks,

Andy

--
DELANO,ANDREW DOUGLAS
Georgia Institute of Technology, Atlanta Georgia, 30332
uucp: ...!{decvax,hplabs,ncar,purdue,rutgers}!gatech!prism!gt3398b
Internet: gt3...@prism.gatech.edu

[Richard George]

Off the top of my head, from A-level Physics :

Each tube will create a range of notes in harmony, but the fundamental note
will be by far the loudest. The wavelength of the fundamental note produced
will be equal to twice the length of the tube, if the tube is open both ends.
Pitch values are normally referred to by their frequency, a standard A as used
for tuning is 440 Hz (ie vibrations/second). Wavelength converts to frequencies
by the formula:
frequency= speed of sound / wavelength
Speed of sound is... ummm... 330 metres per second, (check that if you can)
so :
tubelength (in metres) = 2 x wavelength = 2x 330/frequency
Unfortunately, the conversion from frequency to note is not simple: To jump up
one octave, you double the frequency. To increase pitch by one semitone, you
multiply by 10^((log2)/12) , which is 1.05946... To drop one semitone, divide
frequency by this number.

So, in pitch, a scale from the tuning A gives:
A 440 Hz
Bb 466.2 Hz
B 493.9 Hz
C 523.3 Hz
C# 554.4 Hz
D 587.3 Hz
D# 622.3 Hz
E 659.3 Hz
F 698.5 Hz
F# 740.0 Hz
G 784.0 Hz
G# 830.6 Hz
A 880 Hz

You cannot guess how relieved I am that that worked out!

So, to take a couple of length examples:
Tuning A has freq 440Hz, so length = 2*330/440 = 1.5 m
Jump the octave: A 880 Hz has length 2*330/880 = 0.75m
Depending on what pitch you want, you may have quite long or quite short tubes.
If the length seems excessive, think of organ pipes. Their pitch is worked out
in a very similar way, but there is a difference because they are closed one
end.

If, as is fairly possible, I've been talking complete rubbish (I don't think I
have), I'll post again to say so. If I'm right, I'll post anyway. Good luck.
NB: I'm an electronic engineer, not a acoustician
--
Richard George, Electro Eng Tripartite, Southampton University.
Homepage: http://whig.ecs.soton.ac.uk/~reg94/index.html
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Talk is cheap because supply exceeds demand.

[Michael A. Casey]

>>I'm trying to make some wind chimes from some aluminum tubing. Does
>>anyone know of equations which relate the tube parameters (ie. length,
>>OD, ID) to the note at which the tube will sound?

This may be a non-trivial problem for an alumin(i)um acoustic tube.
Typically, a waveguide solves the wave equation for a wave traveling
inside a duct. In this case relating length to frequency is simple,
Fundamental frequency = c/(2L), where c is the speed of the wave in the medium
(approx 340 m/s for air) and L is the length of the tube in meters. The complex
modes of the vibrating system determine the harmonic structure, but it is guaranteed to be
periodic because of the reflection of the wave at both ends of the waveguide duct.

However, for a wave travelling along the cylindrical tube itself, it seems that the problem
is much harder. The complex modes of this system give rise to an inharmonic spectrum that,
by definition, has no fundamental frequency that is the difference frequency of the individual
harmonics. Thus the "perceived" fundamental is difficult to calculate.

I know about waveguides, but I don't know much about the modes of vibration of cylinders.
You may need help from sci.physics.acoustics.

PS. Does anyone know the piece "windchimes" by Denis Smalley? It's on the Wergo Label,
Current Directions in Computer Music series #5 (I think). Worth a listen.

Mike Casey
Machine Listening Group
MIT Media Lab
Cambridge MA
http://sound.media.mit.edu/~mkc
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-=-=-
Michael Casey [http://sound.media.mit.edu/~mkc]