Hi Jurgen. Breaking strength is also dependent on some other bits and pieces of wire physics, in particular the Youngs modulus. I spent a couple months trying to figure out with my own limited math and physics how both the Youngs modulus and the string density figures could be so different depending on where you looked.... and how they actually worked out in some of these formulas. Again, using McFerrin... this time the inharmonicity for plain wire given there. It became apparent to me that looking at equation 4-2 on page 43 that one could calculated Youngs modulus directly from String density... or the other way around depending on what was <<known>> ahead of time. I posted quite a few querries on the matter a year or so back because doing so seemed to be exactly what Robert Young himself did in his own paper on the modulus and yet in real life you not only run into wildly variant values for Youngs modulus and average density for piano wire is, but if you plug in the values for other potentential string material the Inharmonicity given by McFerrin no longer seemed to work. I talked a bit with the author of Bonemens about this and he citied this as one of his main reasons for not even bothering including bass strings in his scaling program. Inharmonicity was dodgey enough for plain wire but for bass strings just useless was his reasoning.... struck me as going a bit too far but just so. In anycase, as to your specific question. The apparent difference in string density given the figures I cited does seem quite low yes, and would as such tend to lead one to think that difference boarders on being less then significant. It is ususal to simply combine the values for PI, String density and acceleration into a constant. That is (PI*String Density / 981)) when Length and diameter is in cm ^2. For regular wire this works out to 0.02513. Pure sound ends up at 0.02530. The tension formula then becomes T = f^2 * L^2 * d^2 * K, where K is the constant just mentioned, and L and D are in cm^2, and T is given in grams of force. I'll leave it to you to see if your 0.64% idea works out in the resultant tension. :) Jauns version of this utilizes tension in Kilograms (a bit more practical as an end result) But then his measurements for L and d are in meters ! and the gravity acceleration is 9.81 instead of 981. I suppose that last bit can get a bit confusing when trying to sort all this out by oneself, as the 981 figure is a specific physics quantity. 981 centimeters per second per second. Also, one gram of force corresponds to 981 dynes of force. Dynes is a physics quantity usually used to express tension... its just folks like piano scalers who find that quantity awkward and insist in using kilograms or pounds instead. Actually guys, Jim you mentioned this about understanding math. I flunked high school maths hated classes. In first years of college I found that I actually did like algebra and took a couple classes and did quite well. But I never really followed up. In my later years I have thrice tried to find time to get back into it because its really just an enormous and fantastic puzzle game... but one has to make a living as well.... so I have managed to get into that pre-calculus stage that all of us are supposed to learn by our senior year of high school. None of the maths or physics I've seen discussed over the years here really even get close to that (with very few exceptions). I would suggest we underestimate our abilities to digest these maths and physics concepts and skills. Setting off a bit of time here and there and digging through ones high school levels books to figure out a problem puts you on the road. Go for it. Cheers RicB My math is probably wrong on this and I'm sure I will be corrected if that is the case. But as I see it, the difference in string density between Pure Sound and standard wire is less than 0.64% Wouldn't that, according to the McFerrin formula, result in tension that is 0.64% higher? And is less than one percent really enough to make a noticeable jump that much closer to the breaking strength? Help me out on this one... Jurgen Goering Piano Forte Supply (250) 754-2440 info at pianofortesupply.com <https://www.moypiano.com/resources/#archives> http://www.pianofortesupply.com
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