Hi Phil, > 1. If the sound is reflected at contact points then it should be possible to > tune the rear duplex longitudinal frequency by moving the aliquot, as CFT > seemed to believe. Would you say that this is correct? Absolutely. In the case of longitudinal/compression waves, this would be similar to shortening or lengthening a tube (e.g. on a slide whistle). > 2. If longitudinal vibration in the speaking length is reflected at the > bridge what would cause a longitudinal vibration in the rear duplex? I just said the bridge and other contact points are a reflection point. That doesn't mean *all* the energy is reflected. Think of sunlight passing through a window pane. This is another case in which the index of refraction (think impedance) varies abruptly between the air and glass and then again between the glass and air. Some light reflects off of the outer surface. Some light reflects off of the inner surface and keeps traveling back towards the outside. Most of the light in that path travels beyond the outer surface to the outside. Some of it reflects again and heads inward. Most of the incident sunlight passes through all surfaces into the inside of the house. This effect can be a real problem with camera lenses, which is why they are coated with substances with lower indices of refraction. Anyway, any combination of contiguous lengths in a piano wire (from contact to contact) can form a resonant pathway. The importance of each pathway is yet another matter. > 3. If these frequencies are so high that we can't hear them is there a point > in doing tuning of the rear duplex for the longitudinal mode? If the vibrations of importance are indeed compression waves through the steel, then I would imagine there is little point. However, as I said, I suspect the true importance would be for tuning transverse waves, just as with the main segment. > I suppose that depends on how you believe the rear duplex is put into > vibration and what effect the vibration of the rear duplex has on the sound. > If the rear duplex is being put into transverse motion by the up and down > movement of the bridge (which itself is a subject of some disagreement on this > list) which is being driven by the motion of the speaking length of the > string, then this transverse movement of the rear duplex would occur anyway, > whether it was muted or not. No additional energy is being sapped from the > speaking length, so to speak, to 'drive' the transverse motion of the rear > duplex. If this portion is muted it is simply dissipating the vibrational > energy of the duplex, not the speaking length. This raises the question - is > vibrational energy in the rear duplex a positive thing? Or the questions - > does this improve the tone? Does this improve the sustain? I believe that > this is one of the essential points of the discussion. I wouldn't think that *much* of the energy is dissipated over time, but surely some is -- enough to affect sustain. In my Wissner, some of the braid is placed near the aliquots contacting both the string and the aliquot. Energy loss would occur there if nowhere else. However, consider that as the bridge and strings vibrate about, the vibrations in the duplex segments would not all remain vertical. When they would occasionally rotate to horizontal, then friction would be introduced as the strings rub against the braid, thus dissipating the vibrational energy. It's not as though this loss of energy wouldn't matter. If vibrations transferred from the bridge are reflected back to the bridge without frictional attenuation, then energy is preserved in the system. (If the bridge were rock-hard stationary, then energy would also be preserved.) However, when vibrations are transferred to the duplex segment and the energy is lost, the bridge must do more work on the duplex segment to keep it in motion, and that work is done using energy from the main segments of the strings. Another way of looking at it is that friction in the duplex amounts to friction in the terminus of the string (considering the bridge/duplex assembly as the "terminus"). This would not be entirely dissimilar to having a frictional terminus (e.g. a finger) on the tuning-pin end of the string. Of course these arguments about vibrational reflection and energy conservation make certain assumptions about phasing relationships... and that's the can of worms underlying the entire subject of duplex tuning. > > objectionable ringing in > > nonspeaking string segments at inappropriate > > frequencies, isn't an alternate > > solution to tune those frequencies to where > > they are appropriate and > > therefore not objectionable? > > This is also one of the main points of the discussion. What do you call > objectionable ringing? I don't know. That's entirely a subjective experience. You folks would be more familiar with a "consensus" model than I would. > What is an inappropriate frequency? probably a lower harmonic. Dunno. Again... subjective > Certain people > seem to think that the rear duplexes need to be 'tuned' and others think that > this is not necessary. There doesn't seem to be any data (other than > anecdotal evidence) to support an improvement in tone (which in itself would > have to be defined) or an increase in sustain (which probably could have a > definition that most of us would agree on) due to tuning duplexes. If you can > do some experiments to provide some there are people on the list who have > expressed interest. <grin> It's quite possible I will find some free time in the distant future and devote some time to measuring these things. Unfortunately time seems to be my scarcest resource these days... besides money, that is. > > I am reminded of a closed field speaker system > > I once designed for my > > research... I > > first attempted this by muffling > > the ends of the tube in order to avoid > > resonance peaks about every 120 Hz.... > >Hopefully the parallels to > > the duplex scale are obvious > > here. Where possible, it seems best to correct > > the tuning, rather than to > > kill the sound. > I'm not sure that the parallels are obvious to me. In the system you describe > it seems that the various resonances are actually sapping energy that is being > input. Muting them would cause even more energy to be dissipated. As I > described above, I don't think that that is the case with a duplex. > Experiment may show otherwise. I look forward to the data that shows me to be > wrong. Resonances don't sap energy. They merely redirect it. The energy remained bottled up in a closed tube and was only dissipated on frictional surfaces which in this system were minimized. In the end, I had a lot of loss from destructive interference, but not nearly so much as from the heavy-duty muffling of prior systems. The reason was that I didn't resort as much to friction to control unwanted sound -- which is the similarity here. Peace, Sarah
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