Jim, Sorry about the delay in my response, but I'm in the middle of transferring to a new computer. I thought I sent this to pianotech but sent it to myself instead... Sometimes hightech is a headache. Although I hate interspersing comments with previous posts, it is the only way to make any sense to all the questions. You wrote : "The longer a given structure is the more potential energy can be stored in it (when the only parameter that changes is the length). If you put a length of wire on the edge of a bench and secure it down right at the edge, with some varying length protruding. Two things will happen. 1. A deflection of equal measured distance at the end of the wire will cause wires of the same size, but different lengths, to vibrate at rates (pitches) but for varying lengths of time. 2. A shorter wire will vibrate faster and for a shorter period of time than will a longer wire." My reply: To make sure I understand you, first assume the structure is a string clamped in a vice and the only change is the length of the "string beam". If you push on the end of the string so that it deflects .020", it will push back to show the potential energy it has stored. If you let go of the string beam, it will vibrate at some frequency. Now lets say we double the length of the string beam. In item #1 of your post you say to deflect the same amount. OK, done. Realize that the force required to do this will be less because the beam stiffness is related to the length. Since less force is required and deflection is the same, the potential energy of string beam#2 is less than the first case. Also, when released it will vibrate at a new frequency because of the longer beam length. 1. If the same energy is imparted to each length of wire is the same, why will the longer wire vibrate longer ? The energy is not the same for the case described above, so the energy release is not the same. 2. Doesn't the longer wire have more potential energy in it than the shorter wire ? Not if beam deflection is the controlling factor. If you would have said to apply the same force to each string beam, then the potential energy would be the same, but the now you would see the deflection of the beams would be much different. 3. Does the shorter wire stop vibrating quicker because it uses up energy in vibrating faster or because there was less potential energy there to begin with. ? The same deflection for two different beams will give different potential energies for the two cases. 4. Would the same factors that apply to open ended wires apply to wire that is captive at both ends ? Generally speaking, yes. 5. Would this captive wire, say size #17, produce more energy at 15 inches of length than it would at would at 16 inches of length? Or vice versa? Same force, similar energy, but different deflections. 6. Isn't the amount of energy potential in a wire determined by the length, weight, and tension of the wire ? Lets change the string beam/vise experiment. Now, we have vices to clamp the string at both ends! If the string has no tension when the vises are tightened, the string beam clamped at both ends will require some force to deflect a distance. If the string has tension in it when clamped, the force - deflection rate will also depend on the amount of tension when clamped. BUT, back to the energy stuff. If the force is the same in the tensioned and un-tensioned cases, the energy stored by the wire is the same but the string deflection will be different. The different tensions will also mean different frequencies when released. Also, the weight of the string is important, but does not mean more potential energy is stored. It will give the string inertia and will be one of the controlling factors in how fast the energy is released (steel vs copper wire). 7. Given the two lengths above, 15 and 16 inches, when either of these wires, equally tensioned, are struck by the same hammer with the same amount of force, say 65 grams, which will deliver the greatest amount of energy to the bridge? Theoretically, it should be the same energy if the hammer velocity (read momentum transfer) is the same. Remember though that since they are different lengths and were pre-tensioned the same, the frequency will be different. Also, the energy transfer is related to structural dynamics, but up till now we were talking about static deflections and forces. 8. Last Question ! If a 15 inch length of #17 wire were pulled to 181 lbs of tension in a nine foot grand and in a 5' 6", grand would there not be the same amount of potential energy in each wire? Where does the difference in volume as perceived and the sustain as perceived come from if not the sounding board? Let's not confuse the potential energy of the pre-tensioned string with the energy the hammer puts into the string. The only way to get any of the pre-tensioned potential energy out of the string is to cut it. Then, the string flies! Otherwise, the energy into the string from the hammer deflects the string and excites the bridge. As far as the difference in a 9' grand and a 5' grand, the longer string would have more potential energy if cut because, although the force is the same the "spring" is longer, providing more reserves to store energy. But again, that potential energy is only available if the string is cut. The same hammer momentum should provide the same energy in the string whether it is short or long. With that is structural dynamics, and now we have a real complex system. I need to go for now but in parting, don't forget we haven't even gotten to soundboard sizes, bridge pin angles, downbearing.... Latter, doug richards drichard@qntm.com San Jose, Ca.
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