Hello Phill,
I am sorry for the delay in responding to your post. Events have made the time for such
activity difficult to come by. Not to beat a dead horse but to reply to the questions in your post,
nevertheless, I do not know which moves first, the board or the bridge and I don't see this as
particularly important as I am firmly convinced, and more so now than several months ago, that if
there is motion of the bridge through such a mechanism involving the strings, it is impossible to
believe that it is at the frequencies of the spectrum of the string. Secondily, were the string
driving the bridge in such a direct manner then it seems a matter of the simplest of physics to note
that there must be a kind of interference between simulataneously sounding unisons which would
render it impossible for the board for the board to be driven harmonically when more than one
unison is sounded, among other problems. This becomes extremely complicated just from this point
alone. I have given an example of an increasing non-linearity of response which is frequency
dependant in the example of the floating of valves in an engine.
Thirdly, the bridge motion view implies that with a string which exerts no pressure on the
bridge or whose downbearing were sufficiently negative a point must be found in which the cyclic
forces upward and downward, or actually in any direction must balance and cancel each other
resulting in a condition in which the string could not drive the board and therefore could not cause
a sound when struck. Were the downbearing made progressively negative the sound should become
correspondingly weaker and a point be reached in which no sound could emanate from the board. This
point cannot be found, nor can the implied alterations in volume be noted. One should try as I did
just the other day a simple test and do such a progressive elimination of bearing. During
stringing it is a simple matter to block up a string rest so that the bearing can be adjusted to
various negative levels and the results observed. . While replacing a treble string on a Baldwin
concert grand with the Accujust hitch pins I cursorily tried this test ten days or so ago, although
I knew full well in advance what the result would be. Pulled up to near tension and listened to
carefully in various positions, the string sounded as expected although the downbearing was ranged
through numerous negative values. This is but another of the subtle troublesome questions attendant
to the pressurists point of view.
As to the importance of the rate of loading consider, if you will, the implications of viewing
all the cyclic displacements of the string during its maximum excursion for each mode of vibration
as occuring simultaneously: that is as a complete system of simultaneous forces: All the
displacements represent forces applied at the same time. For any displacement x the string must
also have a displacement at -x. The resultant of all of the forces generated by the string must
be the original, undisturbed, unvibrating position of the string. The change in the bridge would
be a cyclic pulsing of the tensile stress in the wire, which could only attempt to pull the bridge
back and forth towards the agraffe. This is a far cry from cycling up and down and really
represents a longitudinal stress wave which would transfer elastically into the bridge, through it
and into the board.
The only difference between this view and what happens in the real world is the time rate of
loading and the implications arising out of the ability of the board to respond to this rate of
loading. As John has pointed out with both example and explanation, the mass and stiffness of
the system means it cannot possibly respond harmonically, whether in phase or not, with the harmonic
behavior of the string. This seems to me to inescapably bring into the analysis the question of
what happens due to this rate of loading. What does happen is a progressive non-linearity of
response.
However, it is obvious by using the incidence meter which I described last month that when
applying a force of similar or even much, much, greater magnitude to the strings in order to
simulate the supposed forces applied by the string during its excursions, the result will be
palpably, plainly, different than that occuring during vibration and once again one is forced
towards the conclusion that the board is sufficiently stiff, massive and so greatly bound down by
the other strings that its reponse under vibration differs with the response observed under a
forced, static deflection even though forces either similar or far greater in magnitude to that
created by the string upon excursion be applied.
Another very critical, salient point is that when the string is prevented from developing its
normal standing waves by having stringing braid applied to it again virtually no motion can be
detected at the bridge even though the string be repeatedly violently struck by the hammer. This
suggests the necessity of considering a differing mode of energizing the soundboard as the braided
string stuck by the hammers exerts essentially the same deflective force, should there be such, as
exerted by an unbraided one, yet the results are blatantly different and to maintain the view of the
pressurists one must accept the preposterous conclusion that the braid is absorbing the energy of
the blow.
As I said last month, don't take my word for it - acquire an incidence meter and try it for
yourself. I bought a new one last month specifically to test this point as the one I first had was
chewed to pieces by a dog two or three years ago. This was the one with which I first tried this
test probably five or six years ago. The new one cost about thirty dollars and is a Robart. Take
your own advice and try some experiments with this device.
As to your question regarding waves or forces, obviously strain is caused by a force. The
internal force in a medium is stress as I am sure you know and I have suggested numerous times that
the cyclical variation of stress to strain is perhaps a better way to look at this. This is the
subject matter considered in Strength of Materials courses. Of course this variation is a wave
but, as has been pointed out, the fact of the wavelengths being so large relative to the sizes of
the components of a piano soundboard/system renders the use of wave concept somewhat ackward. I
avoided using the term wave at the very beginning of this discussion for this reason and several
others.
Your summary seems to be fairly accurate overall, but continues a kind of attention to, what is
to me, some irrelevant detail, with all due respect to you, that seems unneccesary. Obviously,
should an elastic wave, that is a cyclic variation in the relationship of stress to strain, pass
first through the bridge, then, dependant upon your definition of motion, the bridge may be said to
move first or no, once again a point I long ago tried to make. That the bridge would be sitting
"still" as you say, I don't know: it is likely to have some motion but this motion is neither
harmonic nor linear, nevertheless, sufficient stillness exists for it to act as a node for the
transverse displacements on the string. The better it does this, the better the sound must be, at
least to my mind.
Also, it is not the standing waves on the string that cause the londitudinal wave to pass into
the bridge but rather the interaction of the standing wave and the bridge itself that transduce the
strain energy in the wire from a transverse displacement on the string to a longitudinal wave at
the bridge where neither spring force nor inertia force act. To grasp this, it seems to me to be a
simple matter to imagine a mark of sufficiently small size placed upon the wire at the exact point
of termination, should such exist, at the bridge pin and notch and then to consider what would
happen to such a mark when the string is deflected. The mark must have some displacement toward the
midpoint of the string and will then tend to return to its original position when the string is
released and passes through the neutral point, the mark will then again move towards the midpoint of
the string as the deflecting string overshoots the neutral point and progresses to maximum
excursion, now 180 degrees different in phase, with the previous excursion, and the mark acting
similarly and so on. The wire undergoes cyclic strain in both extension and compression, that is a
longitudinal wave exists at the terminations and this is the stress transduction method I have
repeatedly advocated.
All the obfuscation nothwithstanding, a similar thing happens in essence with a tuning fork,
although I don't wish to take up this subject with those who can't or won't even make the minimal
effort needed to understand the very simplest aspects of differentiation or integration which helps
shed light on these subjects, much less the abundant utility of differential equations. Insofar as
who is in my camp such a thing is meaningless to me but it should be understood that the extension
of the concepts of the traveling wave on a one dimensional string, its reflection, its constructive
and destructive interference and superposition resulting in standing waves, free vibrations, modes,
or resonances, to a two dimensional membrane (which obviously the soundboard assembly is not) with
its standing waves, free vibrations, modes or resonances, or a three dimensional volume with
similar standing waves, free vibrations, modes or resonances, all compounded in complexity with the
characteristics of forced vibrations, is in no way, shape or form, original with me, although, I and
J.D. appear to insist upon the suitability of this model with but little company on this list.
I have repeatedly said that I can't see the board, responding linearly to a string, or
responding at 440 herz to a string vibrating at 440 hertz. That a bridge, given the right kind of
mechanical driving, could be moved at 440 herz or other frequencies is by no means hard to see. I
have never said the bridge does not have the ability to follow a force at 440 herz or any other
frequency were sufficient driving done. If your plunger is fastened to the bridge, and the forces
applied are of sufficient intensity then it will either break the attachment or move the bridge and
flex the board. Standing waves could easily develop in the board as they are not a function simply
of longitudinal traveling waves by any means, and, surely, you don't mean to suggest I maintain that
they are. Why would you think that I would claim that a bridge, driven by a plunger or rod as you
say, would not move? Or that a sound would not be emitted at the driving frequency in this case.
But this is not the case of a stretched string. If the board were driven at 440 then the emitted
sound should be essentially 440. How does this have anything to do with a node? And where would it
"confuse the frequencies produced by the system"?
If the board were coupled adequately to the plunger obviously it could be driven at many
frequencies. As to where its ability to respond linearly to the driving frequency would begin to
change I don't know in this context, but it would be inevitable as the driving frequency is
increased. Although I don't wish to identify myself with camp one, with all due respect, in this
matter, I have to agree that a tone would be emitted. It is in the behavior of the
soundboard/system with strings attached to it that I differ so substantially.
In regards to your plunger experiment what do you believe would occur were you to drive a point
on the bridge at 440 and and adjacent point at 450?
Regards, Robin Hufford
Phillip L Ford wrote:
> Date: Wed, 30 Jan 2002 22:01:33 -0800
> From: Robin Hufford <hufford1@airmail.net>
> Subject: Re: Sound waves(The behavior of soundboards)
>
> You misconstrue my assertions in regard to motion as I have not maintained that is
> > does not occur. Rather, I say that substantial motion at the string bridge interface
> > induced as a result of the bridge attempting to follow the so called cyclic loading of
> > the board by the string during its excursion is detrimental to the sound as it will
> > displace the node and thereby confuse the frequencies produced by the system. The
> > actual motion of the bridge is elastically induced through the development of standing
> > waves in the bridge/soundboard and, depending upon the particular piano, may be
> > substantial or otherwise. These are two different matters. I maintain that the
> > "cyclic pressure" proponents mistake one for the other.
>
> >The Cyclic Pressurists belive that the flexing string lifts, pushes and pulls upon
> >the bridge as a result of a force produced during the excursion they take the standing
> >waves to be. They have been repeatedly explicit on this point, indeed, posting just
> >today declarations as to these operations and, in particular, contending again the
> >irrelevance of loading.
>
> I believe this is all restating what can be summarized as - which moves first, the
> bridge or the soundboard. This has been a point of contention from the start of this
> discussion. One the one side, as you say, is the camp that says the string moves up
> and down (and all around, but for purposes of this discussion let's say up and down),
> which causes an up and down force on the bridge which causes the bridge to move
> up and down in response (albeit with a phase lag at certain frequencies) which is
> moving the soundboard up and down since the bridge is attached to it. Or to put it
> more simply, the bridge moves first and the soundboard follows. I don't think that
> anyone has tried to deny that this is the point of view of camp one.
>
> Now camp two (that's you, and anyone else who is camping with you - I haven't
> heard anyone speaking up) I believe, if I understand correctly, holds that the
> soundboard moves first and the bridge follows. The actual mechanism of this is
> not completely clear to me. I'll try to summarize what I think I have gathered.
> The standing wave on the string is causing longitudinal waves (should I be saying
> waves or force here?) which transfer to the bridge (which is sitting still, because
> it is at a node) which transfer to the soundboard which cause standing waves to be
> set up in the soundboard which causes the soundboard to move which then causes
> the bridge to move because it is attached to the soundboard. Is this a fair summary?
> If not, please correct or add as you see fit.
>
> You have repeatedly said that it is hard to imagine or believe (am I using the right
> words here?) that a force can cycle at say 440 hz and that the bridge could possibly
> follow. I'm not sure why this is harder to believe than to believe that longitudinal
> waves are flowing in and out of the bridge at 440 hz and causing something to happen
> in the soundboard which is then moving the bridge. Or for that matter, harder to imagine
> than the string itself moving up and down at 440 hz. All seem equally fantastic to me.
> But as Faraday said:
> “All this is a dream. Still, examine it by a few experiments. Nothing is
> too wonderful to be true, if it be consistent with the laws of nature, and
> in such things as these, experiment is the best test of such consistency.”
>
> So, I would like your comment on an experiment. Let's eliminate the string for the
> moment. Take a plunger or rod and fasten it to the top of the bridge. Move it up
> and down at 440 hz or whatever frequency you choose. In your opinion, consistent
> with your view of the way the system works, what should happen? If I understand
> you correctly the bridge shouldn't move in response to the force since the bridge
> doesn't have the ability to follow a force moving up and down at 440 hz. Since there
> are no longitudinal waves being introduced into the bridge then the soundboard
> should have no standing waves set up in it and thus would not itself move or move
> the bridge. There should be a couple of observable results of this. The bridge should
> have no observable motion. No sound should be emitted. If some movement should
> inadvertently occur or some sound should inadvertently be emitted it should not be
> at 440 hz since ' displace the node and thereby confuse the frequencies produced by the system'.
>
> Would you agree with this assessment? If not please comment or correct as necessary.
>
> I believe the view of camp one would be that the result of this experiment would be
> an observable and measurable deflection of the bridge in the vicinity of the plunger.
> A tone of 440 hz would also be emitted by the soundboard.
>
> By the way, the choice of test frequency raises another question. You have talked
> before about the nature of loading. I've never been completely clear on this but
> I have taken this to mean that the system will respond differently to dynamic
> loading than to static loading. I believe that you are in agreement that if you
> displace the string or apply a load at the top of the bridge statically then the bridge
> and board will deflect, are you not? At what point does the bridge and board stop
> behaving in this fashion? 1 hz? 10? 1000? This would influence the choice of
> frequency for the test.
>
> ---
> Phillip Ford
> Piano Service & Restoration
> 1777 Yosemite Ave - 215
> San Francisco, CA 94124
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