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The tension is more or less constant across the strings (about 80 kg if I remember), so that the frame is balanced. But certainly linear mass is not constant (it could not cover such a wide range otherwise), the steel core is wired with copper in the lower strings to add mass.
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((except there are only 7 notes in the diatonic scale, or really 12 in an octave in western tuning systems, and the name "octave" comes from counting the first note twice))
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What about the shape of the bell on brass instruments? I guess it would be some conic curve (hyperbolic?) because it involves reflection, but I couldn't find anything on the subject
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About exponential indeed (impedance match with zero reflection in). http://mafija.fmf.uni-lj.si/seminar/files/2013_2014/The_physics_of_the_trumpet_(Bostjan_Berkopec).pdf … See book by Fletcher/Rossing
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If you want to hear piano octaves, check here...http://www.gootar.com/piano5/piano-chord.php …
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The string or thread tension is directly responsible for the amount of energy (vibrations). You can have a bunch of piano or guitar strings - all the same mass - but they can also have different tensions. The different tensions would give them all different energies when plucked
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Energy comes from tension. Regular thread tension formula... Tension = velocity squared x mass / Length. Plug in c, rearrange, get the one-inch equation for gravity, light, energy and time... TL = mc^2 | -- inch -- |http://www.mccelt.com/quantum-boom-theory.php …
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