Hi Robin, You're right, of course. Yes, there is a true longitudinal wave, but I don't think the "true" longitudinal wave has much importance, owing to the infinitescimal longitudinal comliance of such a short length of spring steel. (It's a bit like the negligible bass response one would get from a speaker a fraction of a mm in diameter, as the microscopic cone just couldn't move much air.) On the other hand, when the front segment of a string is displaced transversely and the rear segment is not, then the bridge is pulled in the direction of the tuning pins. That's significant longitudinal movement (at least in the sense of sound), and it is made possible only by the enormous mechanical advantage in that system. This phenomenon would be characterized by a mixture of longitudinal and transverse waves, far more significant than the longitudinal waves alone. Add to this that transverse waves *must* cross the bridge, as transverse bridge movement is driven by transverse string movement. I really question the importance of longitudinal waves alone, even though I admit they are there. Anyway, I've enjoyed your postings. They have given me a few more insights into string behavior -- not my specialty of acoustics, admittedly. (My specialization is more in the dispersion of airborne sound.) We may disagree or agree as to how vibrations traverse the bridge or how to attribute the terminology, but I think we agree it happens. Anyway, thanks for your input! Peace, Sarah ----- Original Message ----- From: "Robin Hufford" <hufford1@airmail.net> To: "Pianotech" <pianotech@ptg.org> Sent: Tuesday, November 19, 2002 4:22 AM Subject: Re: S&S D Duplex > A correction of one of the, unforntunately, frequent typos in postings of late. rh > > There is a reasonable analogy to drawn between the flexural, bodily, > behavior of the tines of the fork and the transduction of this to a cyclic > vibration or stress wave passing through the(STEM )(corrected version) and the > flexural, standing waves on the string which are transduced similarly by the > terminations at the > bridge/board and agraffe/capo interface. > > Robin Hufford wrote: > > > Hello Sarah, > > The "pseudo-longitudinal wave" is, in fact, a true longitudinal wave but it > > is a forced vibration and contains the frequencies of the forcing function. It > > is the normal mechanical wave or density fluctuation passing through a medium > > as the particles of the medium oscillate around their equilibrium positions in > > the waveguide which, in this case, is mostly the continuing portion of the > > string threaded across the bridge, the bridge itself, the bridge pins, or the > > part of the wire passing through the agraffe, along with the agraffe, Capo bar > > and plate. This is not a variation in tension but, rather, again, a density > > fluctuation passing through the medium with a wave velocity which is a function > > of the inertial and elastic properties of the medium itself, imposed upon this > > is the frequency and extent or lack of periodicity. > > This can be viewed in another way and that is as a state of cyclic stress > > passing through the medium. > > Not to be too repetitive on the list as this has been thoroughly explored > > in the threads referred to earlier, although vehemently disagreed with by others > > here on the list: this can be easily comprehend by considering the behavior of > > a tuning fork. The tines oscillate back in forth at a right angle with regard > > to the stem. Their flexural, oscillating, bodily behavior is mechanically > > transduced to a cyclic stress, strain, or density fluctuation, as you will, > > which is a forced vibration passing along the bass and stem of the fork. When > > placed in contact with the bridge, and it matters little where, this vibration > > then passes into the bridge and board where reflexion, superposition and its > > attendant interference, both positive and negative create distortional and > > dilational waves in the board itself; momentum is then radiated away as acoustic > > radiation. Precisely the same thing happens with the vibrating string itself: > > the standing waves are enabled by the, essentially, rigid termination > > mechanisms which transduce the strain energy associated with the standing wave > > behavior in the wire into forced longitudinal vibrations at the terminations. > > There is a reasonable analogy to drawn between the flexural, bodily, > > behavior of the tines of the fork and the transduction of this to a cyclic > > vibration or stress wave passing through the tines and the flexural, standing > > waves on the string which are transduced similarly by the terminations at the > > bridge/board and agraffe/capo interface. > > The longitudinal wave energy, at the frequency of the forcing function, > > passes into the bridge with out need of flexion, although I have never argued > > that flexion is completely absent for several reasons, and, crosses the bridge > > and continues along the duplex where again, reflexion and superposition create > > audible, tunable vibration. > > I don't know whether these segments increase sustain or not, although, I > > have no doubt that, in some cases, the difference in total sound, as I said in > > the previous post, increases the perceptibility of the note produced by the > > speaking length, possibly in a kind of gestalt/figure interaction. This would > > be very difficult to pin down, accurately. > > This view, which is rather unpopular here, requires a subtle distinction to > > be drawn between the flexural, bodily behavior of the vibrating portion of some > > object or structure, and the nature of wave motion, or, again, localized > > density fluctuations which pass through a medium and do not require actual > > bodilty motion of the medium itself for their propagation. These are just the > > normal, ordinary mechanical waves encountered everywhere. The function of the > > soundboard and bridge stabilize the endpoints of the string and allow the > > transduction through mode conversion of strain energy of the standing waves > > which are of course, primary, but, in another sense secondary phenomena. > > Regards, Robin Hufford > > > > Sarah Fox wrote: > > > > > My other attempted post, accidentally directed to Robin Hufford in > > > private... > > > > > > ----- Original Message ----- > > > From: "Sarah Fox" <sarah@gendernet.org> > > > To: "Robin Hufford" <hufford1@airmail.net> > > > Sent: Monday, November 18, 2002 3:35 AM > > > Subject: Re: S&S D Duplex > > > > > > > Hi Robin, > > > > > > > > OK, thanks for explaining the "longitudinal" wave to me (i.e. which isn't > > > > really a longitudinal/compression wave at all). Steinway's "longitudinal" > > > > wave, if I understand you, is little more than the variation in tension of > > > > the wire as it vibrates, resulting in lateral forces (in direction from > > > > tuning pin to hitch pin) across the bridge. Correct? I would think there > > > > must also be some transverse (e.g. vertical) vibration in order for > > > cyclical > > > > tensional variations to result in any sort of string vibration. Really I > > > > view the pseudolongitudinal wave (as you explain it) as yet another aspect > > > > of a transverse wave. Of course I'd need to think about it... and my > > > brain > > > > doesn't work all to great at this time of night. <yawn> > > > > > > > > I suppose I would still echo Del's concern: Does a pseudo-longitudinal > > > wave > > > > travel to the duplex segment through the wire or through the bridge? I > > > > would argue that unless the string slips freely on the bridge pins, which > > > it > > > > clearly doesn't, that the bridge would have to move in order for > > > vibrations > > > > to pass into the duplex segment. I don't think there's anything magical > > > > about it. On either side of the bridge, we're still talking about > > > > garden-variety transverse waves, which are tunable in every sense to which > > > > we have grown accustomed. > > > > > > > > As I see it, the fundamental questions are still: > > > > > > > > (1a) Does an unmuted duplex segment increase sustain? (1b) Does the > > > tuning > > > > of an unmuted duplex segment affect sustain? > > > > > > > > (2a) Are the tonal effects of a duplex segment desirable? (2b) How does > > > > this differ between tuned and untuned? > > > > > > > > The first question can be answered quantitatively. The second is a > > > > subjective matter, not unlike the age-old argument as to whether a large, > > > > echoing concert hall sounds better than an "anechoic" chamber -- or vice > > > > versa -- or some compromise inbetween. Different strokes for different > > > > folks. > > > > > > > > Anyway, thanks for explaining what is really meant by this "longitudinal > > > > wave" thing. It makes much more sense now. > > > > > > > > Peace, > > > > Sarah > > > > > > > > > > > > ----- Original Message ----- > > > > From: "Robin Hufford" <hufford1@airmail.net> > > > > To: "Sarah Fox" <sarah@gendernet.org>; "Pianotech" <pianotech@ptg.org> > > > > Sent: Monday, November 18, 2002 3:35 AM > > > > Subject: Re: S&S D Duplex > > > > > > > > > > > > > Hello Sarah, > > > > > Distinctions should be drawn on the subject of > > > > string/bridge/soundboard > > > > > behaviors which take into account not only the difference between > > > > transverse > > > > > waves on the string and the possiblity of longitudinal waves there also, > > > > but, > > > > > additionally, the mechanical function of the soundboard/bridge and > > > string > > > > > interaction and the nature of relevant forcing functions themselves. > > > > > The standing waves on the string itself do not move across the > > > wire, > > > > nor, > > > > > in my opinion, do they "rock" the bridge up and down significantly. > > > > Rocking is > > > > > not necessary to transfer energy into the bridge or past it to the > > > duplex > > > > > segments, bridge, soundboard, agraffes, plate or whatever. Another > > > > mechanism, > > > > > which I called "stress transduction" in a very intense, controversial > > > > discussion > > > > > of this same subject earlier this year will easily account for this and, > > > > > although it seems to be well understood by only a few, is available on > > > > the > > > > > archives under the subject lines "The behavior of soundboards" "Rocking > > > > > bridges" and others which escape me at the moment. > > > > > Briefly, at the terminations of the string the wire itself is > > > > subjected to > > > > > a periodic stress induced in it by the cycling standing waves occuring > > > on > > > > the > > > > > speaking length segment and their interaction with the > > > bridge/soundboard. > > > > > These are separate from the traveling waves developed on the wire by the > > > > hammer > > > > > which superimpose to create the cyclic standing waves on the string. . > > > > The > > > > > resultant of the excursions made by the standing waves is along the > > > > equilibrium > > > > > point of the wire and, at the terminations, a periodic stress is > > > > experienced by > > > > > the, essentially, immobile wire segments there, held down there as they > > > > are by > > > > > the vastly greater forces of the other strings, the downbearing, etc. > > > > This is > > > > > not a free vibration of the wire but, rather, a periodic, mechanical > > > > stress wave > > > > > which passes easily across the terminations whether bridge pin or > > > > agraffe. > > > > > Touching a tuning fork to the bridge results in essentially the same > > > kind > > > > of > > > > > stress transduction. > > > > > In the context of the duplex segments, which, in my experience are > > > > not > > > > > necessary for a great sounding instrument, witness some Chickerings, > > > but > > > > which > > > > > may well exist on one, it is important to understand that the energy > > > > passing the > > > > > terminations is a forced vibration; that is a periodic state of stress > > > is > > > > > imposed which has the frequencies contained in the string, and not a > > > free > > > > > longitudinal vibration. I think Steinway grasped this distinction only > > > > poorly > > > > > but refers, albeit clumsily, to it with the term longitudinal > > > vibration. > > > > As > > > > > you point out, the frequency of a true longitudinal vibration in the > > > > duplex is > > > > > dependant on the lengths and wave speed of the medium, and this > > > produces > > > > > frequencies far too high to be much relevant to normal piano sound. > > > > > The distinction between a kind of pseudo-longitudinal forcing > > > > function > > > > > which describes a state of stress and the ordinary, longitudinal wave is > > > > > critical, I think, to understanding the intended value of the duplex. > > > > Speaking > > > > > as a pianist, I never know whether a piano has a duplex or not unless > > > > there is > > > > > sufficient whistling and jangling to draw attention. If a piano is > > > like > > > > this, > > > > > usually, there are so many other things wrong with it that these > > > > imperfections > > > > > are merely a few of many and the connection with the instrument is > > > > lessened. > > > > > However, many times while tuning I have looked down at the front duplex > > > > segment, > > > > > silenced it with the touch of a finger, and immediately noted a kind of > > > > drier, > > > > > dull, sound. > > > > > The stress wave, or pseudo-longitudinal state of forcing, passes > > > the > > > > > terminations or bridge into the duplex segments where a similar > > > reflexion > > > > and > > > > > recurrency of effect as occured in the superpositions of the traveling > > > > wave in > > > > > the speaking length occurs, resulting again in a transverse set of > > > > standing > > > > > waves which, of course, are greatly attenuated. This can be tuned by > > > > moving the > > > > > duplex. > > > > > Additionally, the transfer of energy into the bridge is easily > > > > accomplished > > > > > both by refraction and mode conversion of the wave type. > > > > > Although it is heresy to some to claim such, in actuality, > > > > approximately > > > > > the same amount of energy leaves both ends of the wire at the speaking > > > > length > > > > > terminations - the difference in acoustic effect of the stress wave or > > > > > condition passing into the plate on the one hand, and into the bridge/ > > > > > soundboard on the other, being, fundamentally, the flexural rigidity or > > > > bending > > > > > modulus which is the product of the modulus of elasticity and the > > > section > > > > > modulus of the material, in conjunction with the degree of reflectivity > > > > and > > > > > size and shape of the medium. > > > > > I believe the utility of the duplex in essence, is, exactly, what > > > > the > > > > > patentee claimed, and that is the tuning of the segments to harmonics of > > > > the > > > > > fundamental of the speaking length and the effect of this on the > > > > sensibility of > > > > > the notes, particularly, those of the treble which need some means of > > > > becoming > > > > > more perceptible than the more instrusive tenor and bass. That the > > > > companies no > > > > > longer take the trouble to tune them is no surprise to me, given the > > > long > > > > > decline of piano building. Numerous other examples exist of features > > > > abandoned > > > > > or in use in name only. This is characteristic of the industry itself. > > > > > However, I do think, judging from what he says, that Ron Overs may be on > > > > to > > > > > something with regard to his method of altering the tuning of the front > > > > duplex, > > > > > that may, indeed be new, in this regard, although I have no personal > > > > experience > > > > > of this. > > > > > Regards, Robin Hufford > > > > > > > > > > Sarah Fox wrote: > > > > > > > > > > > Hi Phil, > > > > > > > > > > > > > 3. If longitudinal vibrations can pass the bridge, it seems to me > > > > that > > > > > > they > > > > > > > can just as easily pass the aliquot. So the aliquot position is > > > > > > irrelevant. > > > > > > > The plate pin becomes the relevant thing. In order to actually tune > > > > this > > > > > > > portion of the string for longitudinal vibrations you would need to > > > > have a > > > > > > > movable plate pin. This feature has not been incorporated into any > > > > piano > > > > > > that > > > > > > > I have seen. > > > > > > > > > > > > Actually every contact point would be a sound reflection point, > > > > resulting > > > > > > from an abrupt impedance differential. If we're talking about > > > > compression > > > > > > waves in the string, which it appears is the implication, the free > > > > resonant > > > > > > frequency between any two contact points would be half of the speed of > > > > sound > > > > > > through spring steel (not through air), divided by distance. It would > > > > be > > > > > > *incredibly* high (bat frequencies and beyond, not dog frequencies), > > > and > > > > it > > > > > > would only be tunable by moving contact points (assuming the spring > > > > constant > > > > > > is indeed constant -- or approximately so). You suggest the sound > > > would > > > > > > stop at the hitch pin. It would not. That is only another contact > > > > point. > > > > > > It would travel into the plate and beyond. It would also have a > > > > difficult > > > > > > time coupling into the bridge, except by rocking it. > > > > > > > > > > > > Personally, the importance of longitudinal vibrations doesn't seem > > > very > > > > > > probable to me. It is easy enough to see how transverse vibrations > > > are > > > > > > coupled into duplex strings from vibrations in the bridge, > > > irrespective > > > > of > > > > > > what Mr. Steinway might have claimed to the contrary. Why invoke > > > > mysterious > > > > > > ultrasonic longitudinal vibrations? Just because Mr. Steinway got a > > > > patent > > > > > > doesn't mean he understood the acoustics of his invention. > > > > > > > > > > > > In the end, could it be that the biggest benefit of a tuned duplex > > > scale > > > > is > > > > > > the "freeing up" of the vibrations of the strings and bridge by > > > > eliminating > > > > > > the need to mute the strings on the far side of the bridge? After > > > all, > > > > > > mutes of any kind work through frictional dissipation of vibrational > > > > energy. > > > > > > Isn't it reasonable to expect that muting adversely affects a note's > > > > > > sustain? If the purpose of muting is to kill 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? > > > > > > > > > > > > I am reminded of a closed field speaker system I once designed for my > > > > > > research. (Think of a tiny speaker in a very long, sealed tube.) The > > > > > > objective was to make it flat (+/- 1 dB) from 100 Hz to 15 kHz and > > > make > > > > it > > > > > > efficient enough to deliver 120 dB SPL to the end of the tube with > > > > minimal > > > > > > distortion products (-60 dB or better). I first attempted this by > > > > muffling > > > > > > the ends of the tube in order to avoid resonance peaks about every 120 > > > > Hz. > > > > > > (Think in terms of "muting" inappropriate frequencies.) I kept > > > muffling > > > > and > > > > > > muffling until I had to deliver so much power to the speaker driver as > > > > to > > > > > > toast the voice coil. (We're talking about an EV1202 ferofluid > > > driver!) > > > > > > Eventually I learned to work *with* the resonances instead of against > > > > them. > > > > > > I removed almost all the muffling and filled the tube with smaller > > > > > > open-ended tubes that were tuned to a variety of other frequencies. > > > The > > > > > > idea was to "resonate at all (or many) frequencies." I achieved > > > enough > > > > > > efficiency to deliver 120 dB SPL at 1000 Hz using only a half watt of > > > > input > > > > > > power! I was up to several watts at 15 kHz, but not nearly enough to > > > > blow > > > > > > the voice coil. In the end, my system achieved the flatness I > > > desired, > > > > > > along with far more efficiency than I had ever hoped for. It was sort > > > > of a > > > > > > "Bose" solution. 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. > > > > > > > > > > > > Peace, > > > > > > Sarah > > > > > > > > > > > > _______________________________________________ > > > > > > pianotech list info: https://www.moypiano.com/resources/#archives > > > > > > > > > > > > > > > > > > > > _______________________________________________ > > > pianotech list info: https://www.moypiano.com/resources/#archives > > > > _______________________________________________ > > pianotech list info: https://www.moypiano.com/resources/#archives > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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