Ron and Del,
It being the weekend I am able to post to the list and comment on the
ripple analogy. I apologize for the length of this post but it is what is
required to express the point.
The ripple analogy is, to my way of thinking, rather inaccurate, or
perhaps I should say, substantially so, as a model for soundboard behavior.
Here is the reason why I think this is so.
A force exerted by some object against some other object must
ultimately cause either translatory motion of the object, rotation, or a stress
disturbance propagating in the object itself and, of course, increase or
decrease its energy as the case may be. As I am sure you know this is
dependant upon the impulse, point of application, center of mass, etc etc
and, in particular, the ratio of the mass of one object to the mass of a
second object.
In contact forces, obviously energy is transferred by the mutually
induced strain of one object by another. For example a ball hit by a baseball
bat will be deformed during the period of contact with the bat which itself
will undergo deformation. Eventually, however, the kinetic energy of the bat
which is substantially greater than that of the ball overcomes that of the
ball whose direction is reversed and the ball then flies away. During the
period of contact substantial strain occurs to both the ball and the bat: this
is the only mechanism of transfer of energy from one to the other. This is of
course, all old hat. The point that I am trying to make is that it is the
ratio of the mass of the objects and the duration of contact that determines
whether the energy transferred will in fact cause translation, rotation or a
stress disturbance in the oject tself.
For example, a mosquito hitting head on an aircraft carrier travelling
in a direction opposite to it when both are travelling at thirty miles an hour
will not in any way affect the velocity of the carrier even though their
closing speed is 60 miles an hour, notwithstanding vector addition, because
the energy of the mosquito on a molecular and atomic level is not sufficient
to propagate a stress disturbance through the carrier that is adequate to
reorganize the individual vectors of the particules which comprise the
carrier. However, the particle velocity of some of the particles on the
carrier will be changed, they in turn transmit a change to others and thereby a
stress disturbance of limited duration passes through a part of the ship which
has gained a little bit of energy, essentially in the form of heat. The
mosquito however, will suffer profound change both in structure, that is as
deformation, and velocity as the vectors of the individual particles, so to
speak, overcome by those of the ship and acceleration occurs.
A similar thing would happen but with the ship undergoing deformation and,
as it were, reacceleration should it encounter something, say the sun, a
planet, a continent, or other structure whose mass was sufficiently great.
The point of all this is that it is the ratio of the masses of two bodies
which are in contact with one another along with the force interacting between
them which determines whether organized motion such as translation or
rotation will result as the vectors of one body overcome those of another, as
it were, or whether a stress disturbance passes through one of the
bodies. The stress disturbance may be periodic or chaotic as the case may
be but if the threshold for imposing translation or rotation is not reached
then translation or rotation does not occur and the energy exchange of the two
bodies in contact is of the nature of stress disturbance.
How does this relate to pianos? The soundboard assembly,- ribbed,
bridged, pinned, crowned, glued in at the inner rim and on the whole vastly
more massive and stiff than a string does not move at the bridge/string contact
point, in my opinion. This is because the ratio of masses is not adequate for
the string to move the board. That is why one can touch the bridge where the
strings cross without killing the sound, even though a mere damper assembly is
sufficient to do so when applied to the string. Excursion of the bridge and
soundboard at this point is neglible if extant at all. One could, I suppose,
call this a ripple but this is misleading and of little significance.
I agree with J. Delacour that a compression wave passes through the board
: this is a stress wave which has, of course, an attendant strain. The
strain itself is the displacement but this displacement is on an atomic and
molecular level as the particles oscillate about their neutral position. There
is no excursion or flexing of the soundboard at this point as the forces
involved are not sufficient to actually move the board, a point which anyone
observing weights placed upon, go bars used, or even people sitting on
soundboards while under repair in shops might begin to suspect.
Depending upon the boundary conditions some fraction of the stress wave,
of course - one should say waves in reference to strings, is reflected back
into the board. At this point things become interesting. In a truly isotropic
medium a stress wave, no matter where initiated in the board, would, for a
given shape and set of boundary conditions be reflected back and pass through
itself, recurrently, in predictable locations; in predictable frequencies and
at predictable amplitudes constituting now a standing wave in the board
itself. This occurs as the superpositions of the stress disturbances result
in progressive augmentation and cancellation of the wave form as the phase
relationships cycle through reinforcement to cancellation.
At this point diaphragmatic motion, that is excursion, takes place in multiple
areas of the board.and this is what designers adjust. The modes and Chladni
figures visualized by the sand technique are visible indications of this whole
process.
Alas, or, perhaps, thankfully, the great anistropy of the board, arising
first and foremost from the nature of wood itself and greatly increased by
variable fletches used in the board, grain angle and orientation, ribbing,
thinning, bridging and binding down at the rim, gives great flexiblity to the
soundboard designer to control the amplitude and relative frequencies of the
modes, which is where actual motion takes place. This has allowed the piano
business of the last several hundred years to arrive a numerous differing
incarnations of sound, in the instruments produced for public sale, something
to my mind that is a true treasure of Western Civilization.
A tuning fork will illustrate handily the nature of displacement and
stress propagation in the same item and is very much analogous to string and
bridge/soundboard. When set into motion the tines of the fork are obviously
moving to and fro; when touched the sound is stopped. This is displacement
and it is greatest at the end of the tines where the stiffness is least. As
one travels down the tines even as the stiffness becomes progressively more and
displacement less the strain disburbance still exists. It is simply expressed
differently. Translation has become vibration. At the base of the tines
there is no motion of the base itself but rather the stress disturbance or,
vibration. One can hold the base of the fork and realize it is not moving in
the same fashion as the tines nor is the sound immediately stopped by contact
with the hand as would occur with displacement. Energy is travelling through
the fork which can be immediately seen if it is touched lightly to another
object. It will vibrate - essentially bouncing up and down.
If you touch this same fork to the plate of a piano one will hear the
sound suddenly much louder, a phenomenon we are all familiar with. This very
same process happens in the plate as happens in the soundboard. It can also
happen on a window, a wall, a floor, - strain energy is loaded into these
things, which propagates, reflects and superposes creating modes which are
again the areas exhibiting real displacement even if extremely slight. In the
case of the plate, in spite of the fact that it is extremely stiff, no amount
of pressure at the point of contact of the fork will prevent this short of
breaking the plate or fork.
Once again, speaking both metaphorically and mechanically the fork is
greatly analogous to the string - it acquires energy from some source and
experiences actual displacement as does the string. The string is attached to
a sufficiently rigid material at the bridge/soundboard/string interface that
this displacement is transduced to strain energy as happens at the base of the
fork. Both drive the board, or anything else, at least mechanically, in a
similar fashion as has been described.
Regards, Robin Hufford
Ron Nossaman wrote:
> >There is also often an attempt to distinguish the vibrations of an elastic
> >medium which is exposed to air, from the vibrations induced in the air by
> >the interaction. Both of these are technically sound waves, since both are
> >vibrations in an elastic medium. The fact that the air can interact
> >directly with our ear, while the soundboard cannot do so makes absolutely
> >no difference. They are both sound. One might say that the interface
> >between the soundboard and the air is a transducer (ha ha), converting the
> >power input from the sounboard to power output in the air...but that may
> >be treading on thin ice after tha past few days here.
> >
> >Stephen
>
> My problem with the use of the word "sound" here was the impression that
> the soundboard works with internal compression waves. While sound that we
> hear by atmospheric transmission is a pressure wave propagation, the
> pressure wave propagation isn't the primary driver of soundboards. It's the
> ripples on the surface of the "pond" that produces the bulk of the pressure
> wave in the air that we hear.
> It's not the word that is the issue, it's the wave form.
>
> Ron N
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