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FREE REED PHYSICS - 2
ttonon posted a topic in Instrument Construction & RepairGreetings again to free reed enthusiasts. In this post, I’d like to show results comparing steel to carbon fiber. In thinking about this issue yesterday, I did a web search and found that people are now selling carbon fiber material in thin sheets – for very reasonable prices. This opens the possibility of experimenting with this material as tongue material. Though, I'm sure some makers already know this. I say this because of the very interesting results from the free reed physics model I’m working on. I put up another .docx file showing the difference between steel and carbon fiber vibration spectrum in the same way I showed for steel and brass, and the link is below. The results indicate that the primary material property that affects tongue vibration is the ratio of Young’s modulus to density. In 2012, I posted a survey of materials that one might consider making tongues from, based on the hypothesis that E/rho is the only material property you need to know as a measure of what the musical tone would be. The link is: https://www.concertina.net/forums/index.php?/topic/14568-reed-tongue-materials-a-survey/&tab=comments#comment-138942 and the original table is still available. That hypothesis is valid rigorously only for the free vibration of the tongue, which occurs after the transients have died out when you start vibration by plucking. I didn’t know what effect it would have in forced vibration; i.e., excitation by a bellows pressure. The physical model I now developed shows that there’s an influence by both E and rho separately, apart from their appearance in the ratio. But now with this complete theory we can calculate the effects of E and rho, along with all the other important parameters, and these calculations give support for the simple idea that the ratio is the primary influence. If we normalize the ratio E/rho for different materials using that for steel (divide all ratios by that for steel), we get 1 for steel, 0.497 for brass, and 6.8 for carbon fiber. There’s considerable variation for carbon, but I think this is a representative value. I’m assuming here that steel sounds brighter than brass, as reported. I assume further that the reason is because steel has about twice the ratio E/rho that brass has. This is true IF the character of these harmonics in tongue motion carry through to the musical tone, and the difference in harmonic amplitude is now firmly established. From the plots, we see that carbon, with an E/rho ratio over six times that of steel, produces higher harmonics that greatly dominate those for steel, even at relatively low bellows pressure. In FREE REED PHYSICS – 1, plots show that higher harmonics for steel dominate those for brass at higher bellows pressure. But with carbon vs steel, the dominance is much more, with carbon favored. As the reasoning goes, we thus expect that carbon would sound much brighter than steel, even much brighter than steel sounds in relation to brass. Of course, I could be wrong, and these tongue vibration harmonics don’t translate to musical tone. I’d be surprised because I don’t see any other way that tongue material could affect musical tone. The fact that players report clear differences in the sound of brass vs that of steel strongly indicates to me that plots such as these can lead to an educated guess on what different tongue materials sound like, just from knowing these two key properties. I did simple calculations on the tongue geometry required for a carbon tongue material. Using available thicknesses (0.5 mm and 1 mm), the lowest concertina pitches would require lengths around 4 inches at 0.5 mm thickness for 100 Hz. These lengths are probably too large, and thinner sheets would be required for shorter lengths. Perhaps the 0.5 mm size could be sanded down. Carbon is a material very easy to work with. The high end is more accommodating, requiring lengths around 5/8 inch at 1 mm thickness for 8700 Hz. A 1 mm thickness is also much thicker than existing steel construction, and that might introduce interesting issues with such short lengths, perhaps in connection with the plate thickness. We can of course now use the model for calculations involving different plate thickness. Another alternative is to make tongues at the extreme pitch ends out of steel. Of course, we can wonder just how bright a carbon fiber tongue could sound, and I encourage makers to give it a try, if they haven’t already. The docx file for Carbon and Steel is at: https://app.box.com/s/zchj1y5d4l65fttok3n4sofupzx2gsio Best regards, Tom