Phillip,
I don't say that there is no applied force from the string. I tried in earlier
posts to indicate the nature of forces applied to the bridge/soundboard, especially
in regard to the nature of loading. Calculating the static loading of the board by
the strings and the point of equilibrium of the board/string system, and this is a
simplification, is obviously the effect of forces. However, the loading of the
bridge itself is better approached by the mechanisms of dynamic loading where, in my
opinion, there are very substantial implications for the design and behavior of
soundboards.
With regard to the nature of motion at the string/bridge interface I have
expressed, to the point of tedium, that the transfer of energy from string to bridge
is essentially through stress propagation. Call this sound, if you will. I
continue to say that any physical motion induced by the so-called cyclic loading of
the system is very, very small, would be detrimental, and that soundboards are in
fact intentionally or otherwise designed to miminize, control or eliminate this.
Were there perfect
rigidity, the wave organizing function of the terminations would be at their
greatest efficiency. However the effect of this ridigity on the soundboard would be
a significant and deleterious matter, as the effect of the bridge on the
soundboard/rib system should in some way facilitate or at least minimize any
counterproductive effects on stress concentration and acoustic radiation.
Local yielding, or local deformation of the bridge in the area of contact with
the string is inherent in the notion of strain propagation. This however, is not
physical, substantial, bodily movement of the bridge itself, that is, motion which
is claimed to be capable of moving the soundboard. It may well happen that
subsequent to the loading of the soundboard by stress propagation and cyclic strain
that the board may indeed cause flexural waves or other behaviors at the bridge but
this is not a motion that is a consequence of the transfer relations between string
and bridge but rather the result of stress concentration in the sounboard/bridge
itself, a different subject altogether. The surface expression in the soundboard of
the waves in it is a matter of substantial complexity which is another subject
distinct from the questions arising at the string/bridge interface.
As to the subject of force with regard to which I have made comments to which,
apparently some have taken offense where absolutely none was intended, I say that
stress is not a force, and when used as such, a certain inadequacy of conceptual
efficiency is inherent in such use. With all due respect to its advocates, I
believe this inadequacy resides also in the prevalent view of soundboard behavior
that is the deflection model, and by this a view predicated on force, mass and
acceleration solely and relating it to the basic equation for mechanical waves, that
is, the square root of the ratio of elastic properties to intertial properties.
Rendering the system analygous to a simple one degree of freedom system such as one
finds demonstrated with the dashpot and spring analyis of harmonic motion so
frequencly encountered in the beginning of texts on harmonic motion is but one
example. Although the factors generated by these introductions are absolutely basic
and necessary of course, their utility to the analysis of soundboards is of a much
greater complexity and a different perspective is required especially regarding
transfer relations of energy from one part of the system to another. As I have said
before, this is not by any means an original view of mine but rather, can be found
in any reasonably comprehensive book on the various aspects of mechanics and
acoustics.
Viewing the string as a force component, that is, a vector which in
conjunction with a vector provided by the stiffness and mass in the soundboard, is
capable of moving the bridge distant to the agraffe or capo vertically is
progressively laden with problems as the frequency of loading increases, that is as
the rate of loading increases. Of particular importance is the general inability of
the system to follow, due to its intertia, this so-called cyclic loading or forcing;
the mutual implicit complications of the effect of this on all of the other strings,
the changes in the effects due to vibrating of the string or not, the fact that I
have reported of pianos built where substantial parts of the bridge, even though
having the strings pass normally across the top of the bridge, and having large
areas not even contacting the board under the unisons: where yet one,
in these areas, cannot tell where the difference lies through the sound, and many
other complications suggest, in my mind, the utility of other approaches. Of
course, statically the downbearing load imposed upon the soundboard system is a
system of forces but to apply vector methods to the vibratory, rapid, dynamic
loading imposed upon it by the string is incorrect.
A very useful and inexpensive device can be had in auto parts stores which can
be used to explore firsthand some of the distribution of sound or stress/strain
relationships in a piano. This is a mechanic's stethoscope - a device which itself
uses longitudinal waves to transmit energy to the ear. The cost is usually under
ten dollars. The stethoscope is like that of a doctor but has a long, thin rod on
the end which is placed in contact with the object in which one wishes to listen to
sound. By using this device and placing it on various parts of the bridge,
soundboard, strings and other parts of the piano, substantial facts can be brought
immediately to light. That is, one can trace the stress trajectory, or sound
through the system. At the bridge/string interface this is, essentially, and at
first at least, in the areas in contact of string and bridge.
One may place the tip of the rod on the vibrating part of the string next to
the bridge, an immediate extinction of sound is heard accompanied by a short rattle.
Placing the tip of the rod on the top of string past the bridge pin and point of
contact of the string at the notch, one will hear a clear sound, similar to that
heard by placing the tip onto the birdge itself. Sliding the tip across the top of
the string as it lies on the bridge, one can hear a slight diminution of the sound
as the rod is brought away from the speaking length. Crossing the second bridge pin
and placing the tip next to the pin, a major reduction of sound is heard, a fact of
substantial importance in its implications. Listening to the sound of the rear
duplex section one may note a still present, yet much reduced sound by contrasting
it with the essential lack of sound of a string of a neighboring unison while the
first examined string still vibrates. One may make similar observations at the
front duplex. The attentuation of sound of a continuous string may be followed as
it rounds the hitch pin. One may contrast areas of the bridge and soundboard and
will be able to trace out the soundfield and soundpaths rather easily. One may
contrast the acoustic transfer of the board with that of the plate, rim, legs, etc.
etc. Numerous implications arise from these observations; they generally impeach
the bridge rocking motion in my opinion.
Although, I have said, I believe further consideration should be given to the
string/bridge interaction and agree with John Delacour in that that question should
essentially be kept separate from the function of the soundboard itself.
What one hears with the stethoscope are stress/strain relationships in the form of
sound, along with their distribution.
It is important that note be taken, at least in my opinion, of the heterogeneous
and particular distribution of the soundfield.
For example, athough I think it likely the bridge motion proponents will
contest this, and I await the next ingenious denial, their ideas would suggest that
the agraffe itself must be moving similarly to the bridge, although on an obviously
reduced scale- that is rocking fore and aft, flexing side to side and moving the
plate underneath it. I rather doubt it. Similarly, the rear duplex, where sound
can be heard by examining the string with the stethoscope, should cause the hitch
pin to be subject to a similar effect. Yet, when one listens with the stethoscope
to the neighboring string very little sound is heard. This occurs as the stresses
in the wire rounding the pin becomes so great relative to the stresses that are
the propagating sound in the wire that they are unable to propagate coherently
through the more intense stress concentration rounding the pin. Numerous areas in
pianos may be noted where similar observations apply.
Where I could not hear sound I don't say absolutely no sound exists, although
that may in fact be the case, I simply am not able to detect it using my hearing.
At some point the coherent nature of energy distribution, which may have the result
of the motion and energy of translation of an object, the motion and energy of
rotation, or a combination of the two, or the motion and energy of wave propagation
or a combination of any of these, will eventually become incoherent and in the
case of mechanical wave propagation be manifested as that which incoherent motion
is, namely, heat.
Regards, Robin Hufford
> On Fri, 11 Jan 2002 00:42:28
> John Delacour wrote:
>
> >PF:
> >>I interpret this to mean that the bridge and top are moving in direct response
> >>to the input from the string.
> >
> >That's a pretty ambiguous statement. The bridge and top are
> >obviously moving because the string has caused them to move, but they
> >are _moving_ at a frequency that is not related to the frequency of
> >the sound generated by the string. It is not this movement that is
> >responsible for the acoustic radiation that reaches our ears. How
> >many times do I have to draw this distinction?!
> >
> >JD
> >
> I can't speak for others John, but in my case you're going to have to keep
> repeating it or rephrasing it until I understand what you are trying to say,
> and I can repeat back to you what I believe you said and have you say
> Yes, that's what I said and what I meant. I haven't been able to do that
> so far. What I thought you had been saying was that the bridge and soundboard
> do not move as a result of applied force from the string. (Aside-If I understand
> Robin correctly he says there is no applied force from the vibrating string).
> The bridge and soundboard only move because some sort of input at the bridge
> causes some sort of wave or pressure which then causes something else
> to happen which then causes the soundboard to move. It has nothing to do
> with string movement.
>
> Now, what I believe you are saying is that the bridge and soundboard do
> move as a direct result of force applied by the string but that movement is
> unrelated to the frequency of the string and has nothing to do with sound
> radiation from the soundboard. Is this what you said and meant?
>
> Phil F
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