Del,
The matter in question is - does the bridge move directly as a result of
the vibrating string and is this the mechanism by which the energy in the string
is transferred to the bridge and thence to the soundboard in the form of some
kind of ripples? When I first posted on this subject I had not reached in my
reading your later post in which you disclaimed, at least to some degree, this
description of which apparently you have had, at least, second thoughts of some
kind. Or is there another perspective? I submit there is and that my posts,
which have apparently put some people to sleep, along with those of J Delacour,
which perhaps have kept others awake, have explained it or at least attempted
to do so.
In the interests of amicable discussion I would have to say however that
as the members of this list are at least able to operate computers and are,
evidently, literate, it is not likely they misconstrue what an accelerometer is
or what it can do although in point of fact the motion itself is not what is
measured but rather the time rate of change of velocity, that is the
acceleration which is, as I am sure you know, a second order derivitive -
velocity being the first. That a soundboard once in vibration would also move
the bridge and both would easily measured as being in motion I am also sure no
one in their right mind would question and JD has been very explicit on this
point.
The process whereby energy is transferred from the string to the bridge is,
once again what is in question and I propose, as I did earlier, that a little
consideration of the behavior of a tuning fork, in isolation and when in contact
with some other medium will be most instructive in this regard. To briefly
recapitulate:
In one and the same object, that is, a vibrating fork we can see
visible indications of stress/strain relationships. On the one hand the
flexibility of the tines when struck allows for perceptible, visible
displacements in the region of their ends. While at the same time, on the other
the base of the tines and stem of the fork represents an area in which the
strain energy, visible in the moving tines, has been constrained by the
progressive increase in stiffness along the tines as they approach the base
to such a degree that the strain is now expressed as a molecular stress
disturbance which propagates through the base and stem and is reflected back up
into the rest of the fork. At the base of the time and in the stem visible
displacement is no longer apparent. Is there energy, periodic behavior? Of
course but on the one hand it is molecular and invisibile at the base and stem
and on the other, while still ultimately molecular, it is demonstrably visible
as more organized, translatory behavior, that is transverse motion, flexion or
whatever. The visible flexion can be easily stopped by the merest touch of a
finger but no human hand can exert sufficient pressure to eliminate the stress
wave in the base and stem that is felt as a vibration. A small, light fork
will, when lightly touched to a surface, in fact jump up and down if held
vertically and this is a visible indication of substantial energy transfer
through strain on a molecular level which, when there is a force for it to
react against, will actually propel the fork upward slightly a number of times.
The original impact against the tine of the fork set it in motion, this
motion is transduced by the effectively increasingly stiff part of the tines and
the base to strain energy on a molecular level, that is a periodic stress wave:
this then passes through base of the tines into the stem of the fork where it
is reflected from an unclamped boundary back into the system. Should the
fork be in contact with a surface of sufficient stiffness or mass density, the
pressure exerted by it be kept light and the fork be kept vertical while in
contact with a horizontal surface then it practically becomes alive as the
action/ reaction of the bottom of the base and the surface itself causes the
fork to undergo translation as the two surfaces propel one away from the
other. This and gravity make the fork appear to be slightly jumping up and
down. . It is especially important to note that the jumping action will be in
the direction of the long axis of the fork and not the transverse direction of
the tines. A plain demonstration of the transduction of the flexural strain
energy to a molecular level and its subsequent transduction to translation has
been demonstrated and is further emphasized by the fact that the translation
is now oriented 90 degrees to the original direction of flexion. As the
pressure is increased, and I believe this corresponds to and is one of the
principal functions of downbearing, although there are others, the force
exerted on the fork increasingly prevents relative motion, which is
progressively extinguished. The transfer of energy is increasingly of the
nature of internal, periodic, molecular deformation - that is periodic strain
or a stress wave rather than relative motion of the two parts. This, in a
nutshell is exactly the mechanism of transfer of energy between the string and
the bridge/soundboard assembly and does not require motion of the bridge to take
place. Any substantial motion of the bridge is, in fact, an impediment to the
efficient transfer of energy.
The fact that the bridge may subsequently be moved by standing waves
induced in the soundboard assembly is self-evident and an accelerometer would
indicate this. The effect of this motion upon the transduction efficiency of
string/bridge contacts is another question but I will state categorically that
the idea that the string or strings of a unison is at least somehow wiggling and
rippling the bridge and the soundboard and that this is essentially the
mechanism of transfer of energy from string to bridge/soundboard is entirely
suspect for many, many reasons.
Had this been the case then even a relatively light pressure upon the
bridge should immediately reduce the loudness of the sound emanating from the
soundboard as it does with the flexing part of the fork and a variable pressure
would introduce variable volumes in the sound. This is plainly not the case.
It is the case, however, that pressure upon the stem and base of the fork does
not eliminate the sound; and this is precisely what occurs when pressure is
applied to the bridge. Obviously, one could say that a pressure sufficient to
destroy the system could be easily generated; evidently these effects would be
different then and these kinds of pressure are not what I am referring to. .
There are numerous parallels between fork and the string where these
effects are exactly the same. The merest touch to the side of the end of the
tines extinquishes the transverse flexion or motion of the tines and its
subsequent transduction to periodic strain and is easily sufficient to stop the
sound. The damper assembly exerting force against the string does exactly the
same thing - using a mere flexible piece of felt it stops the transverse, at
first visible motions of parts of the wire, readily and easily. The subsequent
transduction is starved and the driving of the board is thereby ended equally
readily and easily.
Surely, no one would argue should the solenoid model be accepted, that is
that the string somehow ripples the bridge to any substantial degree, that the
extinction of sound occuring when a damper is let down onto the strings could
possibly be the result of what would essentially be the reverse of what you and
Ron appear to advocate - that the damper is sufficient to operate as a
counterweight to a rocking and rolling soundboard, particularly with a flexible
felt interface moderating the force and effect of the damper assembly. It
seems far simpler to suppose that the string is, in fact, driving the board in
a manner that does not contain the troublesome questions implicit in the
solenoid model; this is the strain transduction method described above and that
when the transverse behavior or motion in part is extinguished then so is the
transduction mechanism that had been driving the board.
One need only make the simple experiment I described earlier using the
fork and the wire, whereby the sound of the fork is transmitted, even in a slack
wire where there is no question of transverse flexion, to a soundboard through
what is unquestionably periodic strain to see this whole process readily at
hand.
Another interesting and salient point to consider is that the fork, when
held at the stem and tapped on a tine will be readily set into motion as the
flexion of the struck tine is transduced at the base and propagates to the other
tine which gets in sychronization with the first. This happens faster than we
can detect without instruments but is once again driven flexion, stress
trajectory, induced flexion and a recurrency of effect which causes the whole
thing to get in a flutter together. The stem, however, is too stiff for the
reverse to occur. Holding the tine or tines and striking the base will not
cause the fork to vibrate, nor will it vibrate when one tine is held and the
other struck. This then, is the paradigm for the string/bridge/soundboard
interaction and that is: driven flexion, stress trajectory; and induced
flexion. The string is driven into flexion by the hammer; it is held clamped by
the bridge, bridge pin and relative massivity of the bridge/soundboard assembly
which causes the flexion to be transduced to stress and stress trajectory;
induced flexion then occurs as a result of the superposition and recurrency of
effect described earlier.
Regards Robin Hufford
> ----- Original Message -----
> From: "John Delacour" <JD@Pianomaker.co.uk>
> To: <pianotech@ptg.org>
> Sent: December 16, 2001 7:43 AM
> Subject: Re: Sound waves(The behavior of soundboards)
>
> > The vibrations cause by the transverse movements of the taut string
> > are passed into the bridge at a point equivalent to the point of the
> > tuning fork pressed against the bridge, and this point in both cases
> > is static and not mobile. From this point the vibration, or
> > molecular disturbance, radiates into the elastic medium that is the
> > beech or box or maple + the steel of the pin and travels as
> > compression waves in all directions as fast as the medium, the grain
> > direction etc. allow. Virtually every molecule of the wood or steel
> > will be displaced and oscillate in response to the kicks and shoves
> > from its neigbours. It is the oscillation of the molecules next to
> > the glue line, excited by kicks and shoves from all directions within
> > the bridge, that will now raise a rumpus in the soundboard. The
> > bridge so far remains unmoved, its internal tranquility severely
> > disturbed but outwardly unmoved, unrippled, unfurrowed.
> >
> > Serious comments only please.
> >
> > JD
> > --------------------------------------------
>
> The accelerometer doesn't care at all about the molecules inside the bridge,
> the bridge pin or the glue line. It measures only the physical acceleration
> and motion of the object it is fastened to. And when an accelerometer is
> mounted to a bridge excited by a string it--when connected to the proper
> measuring and/or indicating equipment--indicates that physical motion is
> clearly taking place. The bridge is physically moving predominately in the
> vertical direction with some fore and aft motion and even a little side to
> side motion thrown in for good measure. Whatever else might be taking place
> inside the bridge might be open to some speculation, but the bridge is
> definately and physically moving.
>
> Del
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