Re: correction, Wire Size Calculations
By Craig Brougher
Haste makes waste. I noticed it as soon as I reread the letter regarding the Shear Modulus explanation. Shear = shearing stress/shearing strain =F/A =1. Shear Modulus = shear/distortion caused by strain given in radians as long as that number is very close to the tan[psi]. So Shear modulus will never equal 1. The point I was making is to get rid of the stiffness. To do that, shear =0, not 1. Sorry. The rest of the explanation is ok, I believe.
One final consideration is this: Strings not only create even harmonics, but also odd harmonics as well as parasitic vibrations as a result of beats between partials which are divided by those inelastic domains we were calling nodes. The way physicists help explain the phenomenon which generates transverse pulses in a string is by "assigning" what they call a "virtual wave" reflection. Graphically, they draw that reflection into the hitch as though it were a solid wall or mirror having the same u (mu, mass/unit length). So not only will you have transverse but also longitudinal harmonics and reflections. I have never seen anyone even approach all the things that are happening within and around a string which has been struck with a hammer.
The string tone generated by pipes requires a second partial almost as strong as the fundamental, whose antinode is at the ends and whose node is in the center of the pipe for both fundamental and 2nd harmonic. This we can see physically in a Kundt tube. And we know that if we can actually watch the effect of these sound waves and plot their nodes, all the time listening to a tone very similar to a string sound, then we know what a perfect string must be able to do. (The frein pipe is built so long and slender and unstable that it blows its harmonic without the frein (ideally). When the frein is placed and adjusted, it splits the wind, creating a strong fundamental and equally strong 2nd.)
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(Message sent Fri 3 May 1996, 14:15:57 GMT, from time zone GMT.) |
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