Hi Stephen Thanks for the first direct reply to this point. Tho there a couple of points I am unclear on and I wonder if you could clarify. It almost seems like you are saying that Youngs Modulus for pianostrings is essentially indeterminable (for all practical matters) and that Youngs Inharmonicity coefficient is in error to begin with. To the later, If you look at the paragraphs surrounding equations 8 and 9, Young clearly states that there is a direct relationship between Q and D. And in your example of Brass, Q (Youngs Modulus) should indeed be lower (then steel) as a result of its higher density. Young goes on in the later part of the paper to take an example from one manufacturer who gives a spec for Youngs modulus that fits nicely that same manufacturers spec for density if one employs the relationship Young describes in/around equation 9 in his paper. So... what is wrong with Youngs paper then...? Why is the relationship Q/p = 25..5*10^10th that he gives not valid ? Thank you kindly RicB >According to Youngs paper of 1952 the Modulus divided by the >density of the string results in a consant (25.5*10^10th). It >appears to me that this constant is supposed to be the same >regardless of material, which would mean that E is the product of D >* this constant. Ric, Young's modulus is not an easy parameter to determine experimentally. Using bulk tensile testing, even with fancy equipment, you can't get a very accurate value, partly because real materials never behave completely linearly (even steel wire). There are additional complications that make tensile testing of wire a very difficult experimental procedure, adding to the inaccuracies in determining the modulus for a wire specimen. It is primarily a material dependent property, but can be affected to some extent by mechanical working (and heat treatments). Consequently, a small range of moduli will be relevant for a given material according to how it has been physcially processed. Accurate measurement of Young's modulus can be done by sonic and similar techniques which measure the vibrations of the metallurgical structure at the atomic level. All are involved and generally expensive. There is no general correlation between density and modulus. Compare brass, denser but the modulus is considerably lower than that of steel. >In any case it seems to me that there is some significant amount >of confusion surrounding Young Modulus and it perhaps is more >important in a practical scaleing sense then we assume. It has little practical use for scaling since it is not a controllable factor in wire manufacture. It is essentially determined by the choice of material. >This fits well with your call to empirical testing for breaking strength / %'s The only way to determine the capabilities of your wire is with tensile testing. Stephen -- Stephen Birkett http://real.uwaterloo.ca/~sbirkett
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