Re: Tonlage des Didgeridoos berechnen
[ Forum: Didgeridoo Allgemein ]
Geschrieben von chris am 16. Oktober 2002 17:55:33:
Als Antwort auf: Tonlage des Didgeridoos berechnen geschrieben von seduser am 15. Oktober 2002 12:57:24:
Hmm... hab was bei mills.edu(Didj List FAQ) gefunden:
Dabei wird der Innendurchmesser berücksichtigt!
----How do you calculate the frequency of a PVC didjeridu?
Length =(V (sound) / (2*freq)) + interior radius of the tube.
For more details refer to Matt Newby's Guide to Making Your Own PVC Didjeridu on the Didjeridu W3 Server.
Also, as explained by William M. Robertson, Assistant Professor, Physics and Astronomy at Middle Tennessee State University.
And another explanation by didj list member Mark Temple and includes a short explanation of conical bores.
2.2.3) How do you calculate the frequency of a termited-bored didj?
Jeff Bavis' theory is thus: "Frequency is 'normally' 1/Time. In the case of a termite didg this needs ammending to 1/DreamTime :)"
And Geoff Brown concludes: Once there termites have been at a stick, the laws of Physics become socomplicated that I dont think any human has yet figured out how to predictthese things. I have seen shorter didjs that play lower than longer ones.Also the overtones that make a nice 10th on a plastic tube vary quite a lotwhen termites are involved. I would stick the the 1/Dreamtime formula, that'llwork well.
Phil Scott has a paper: "('Acoustics of the Australian Didgeridoo' by N.H.Fletcher, more info available to anyone interested), the taper of a typical termite didg certainly affects the fundamental frequency, as does the internal diameter. He gives the following equations:"
Call the diameter of the narrow end d0, and of the wider end d1. The effective length, l, of the pipe is the actual length plus an open-end correction of 0.3*d1 - that could be the diameter effect mentioned by some in this discussion.
Now, we define a taper parameter, g, for the pipe thus:
g = (d1 - d0)/d0
He now gives two equations due to Morse (1948) and Nederveen (1969) for the resonant frequencies of the pipe.
Morse shows that for small taper (g less than about 0.2), the frequency fn of the nth impedance maximum is given approximately by:
fn = (c/4l)*[(sn -1)**2 + (8g/(pi**2)]exp0.5
where c is the speed of sound in air. Thus for a cylindrical pipe (g = 0), the lowest mode corresponds to a quarter wavelength in the pipe, and successive modes have frequencies in the ratios 1:3:5:... When the taper is finite (g > 0), the mode frequencies are slightly raised, the lower modes being the most affected. The mode frequencies are thus less widely separated than for a cylindrical pipe.
Nederveen's analysis, which applies for all values of g, shows that the node frequencies fn appear as solutions to the equation:
2*pi*f*l/c = n*pi - arctan(2*pi*f*l/g*c)
"Fletcher comments that for intermediate values of g, the frequencies can be found by solving Nederveen's equation numerically.
The results are similar to those from Morse, basically that a taper raises the frequency of the fundamental while raising the frequency of the higher harmonics in somewhat less proportion. Personal comment: I guess this is one of the reasons that higher modes (the "toot" effect) seem to sound much nicer in highly tapered didges than in straight pipes.
Elsewhere in his paper, however, Fletcher comments on the possibility of perturbations in the bore of the didg affecting the frequencies in unknown (and unknowable!) ways. I guess that's his way of allowing that, for a didg, freq = 1/dreamtime...."
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