Sound waves(The behavior of soundboards)

[Robin Hufford]

JD and Ron,
     To my way of thinking the solenoid model of the string/bridge/soundboard
interaction fails substantially for numerous reasons.  I believe, however,
judging from the quality of argument of its proponents that when their newly
installed soundboards,  rescaled and remanufactured, glistening in the light
are heard they probably sound pretty good, and may well be extremely good
particularly as regards transition problems, and I look forward to an
opportunity to hear one or more them.  I applaud their efforts,  respect them
for it, and am more than happy to see such things.
     However, what I take issue with in the discussion of these subjects in
the last year or two  is the implication that all other  methods, including
the vast compendium of practical knowledge acquired  through the painstaking
efforts of ten or fifteen generations who, in the aggregate have produced far
more pianos than the present generation, and certainly filled the world with
a variety of remarkable designs and  hi-quality instruments which represent
original, remarkable and unique solutions  to the problems of piano design
whatever they are but of which there must be some consensus as we are able to
recognize them as pianos, has in fact been superseded and the efforts of the
designers of the past are all obsolete,  irrelevant and inferior.  This, I
think, is hubris and plainly incorrect.
     The solenoid/loudspeaker model, even if inaccurate from my point of
view, lends creditablity to the impedance concept, which, I think was used
mainly in the past in connection with electrical circuits and has been
steadily gaining creditability for other applications and for this reason
alone, the solenoid model has had a utility.  Even though I am not much
conversant with electrical circuits I know that electrical impedance is the
ratio of voltage to current  and the lag of the two in a circuit.
     I am however, or at least I like to think so, rather substantially more
informed as to mechanics per se, and can say that we
 do not have to throw out the baby with the bath water should the solenoid
model be inadequate to explain the behavior of the soundboard assembly under
vibrating strings.  Happily, we have various  mechanical versions to use,
such as  mechanical or characteristic impedance, which is a complex quantity
of which the real part represents the ratio of  the particle velocity and
pressure of one medium to the particle velocity and pressure of another,  the
two being in contact with each other and energy being propagated from one to
the other.  As such it is a measure of energy transfer and reflectivity  from
one medium to the next and requires recourse to particle velocity and
momentum, that is, essentially velocity and momentum at a molecular level
although the particle itself is a kind of mathematical fiction necessary to
simply the analysis.     This is where, in my mind at least we are in this
discussion, and it is a subject well visited in abundant courses and texts.
     The use of the word impedance has gained a kind colloquial cachet here
as a metaphor for resistance to motion, perhaps as a result of the
proliferation of the solenoid model.  Although in fact it is a ratio rather
than a magnitude of resistance to motion this nevertheless has a kind of
utility as a descriptive term for stiffness in the soundboard assembly and I
have no objection to it and consider it useful.  It is useful to note, once
again, though,  that these functions are expressed in terms of particle
velocity, pressure, and momentum not flexure or deflection both of which are
another subject.  So whether it has to be tested or not, it seems to be well
understood in certain circles.    Also, it is the ratio of the two
characteristic impedances of the media themselves which is the most important
quantity for determining the nature of reflection and transmission at a
boundary.   The impedance ratio, r, is again an expression of particle
velocity and pressure.
     In arguing so strongly against what appears to be very deeply held
beliefs on the part of some, no offense has been intended, even if,
sometimes, the words appear overly strong.  This is just an attempt to
explain a differing point of view.
Regards Robin Hufford



Ron Nossaman wrote:

> >And there is the profound difference between us.  I do NOT see a
> >string physically moving and rocking a bridge and driving the board
> >as a solenoid drives a cardboard cone.  I contested the analogy from
> >the very beginning and do so now.
> >
> >Did I ever say the soundboard does not move?  That would indeed be an
> >odd statement. Did I ever say the bridge does not move?  Since the
> >bridge is glued and screwed to a flexing soundboard, that would also
> >have been a pretty tricky position to maintain.  I said neither.
>
> Then I fail utterly to see how the soundboard can move without the bridge
> moving, and indeed the whole purpose of this.
>
> >What I do suggest is that nothing moves at all until those vibrations
> >or molecular disturbances or compression waves cross the glue line
> >into the soundboard.  At that moment, things get a-movin' an
> >a-shakin'.
> >
> >JD
>
> Which seems to be unprovable one way or the other, and is of what
> consequence  to the workings of the soundboard anyway?
>
> Ron N