Ron,
Ron Nossaman wrote:
>
> <How do you feel this specifically supports your position that the string
> does not directly move the bridge?
>
> Floating of valves in an engine was offered as an example of a system
> that can operate on the one hand as a linear system and on the other as one
> which has non linear characteristics for reasons that are in part similar to
> those occurring in a piano, in particular the forcing frequencies. This
> demonstrates the point I continue to make which you and others prefer to
> ignore, that is, the relevance of loading. You discount the importance of the
> nature of loading in both cases, from my point of view, and express, by way of
> repetition, essentially, what my post indicated but with no regard to its
> implications in the case of a piano. The resonance of either system is but one
> part of the response curve and is not particularly important as regards this
> point.
>
>
> I have attempted to support my view with established principals of physics
> that can be verified easily enough in many many physics and vibration
> references,
I daresay I have done the same with similar use of physics and its principles.
It is a measure of the possible futility of this discussion that you seem to
unawares of this.
Believing, along with others as you do, that the string is pulling and
pushing the bridge and then moving the soundboard would you then agree that the
string should move the bridge and board downward when the string is pressed
down, and similarly upwards when lifted? If you do agree, then would you also
agree that this is the mechanism, although perhaps simplified, that causes the
subsequent wave behavior in the board that results in acoustic radiation? You
have said so, essentially, many times.
How do you suppose this can occur efficiently when the string is not
effectively clamped to the bridge by the bridge pins? The frequent traveling up
the bridge pin by the strings on a grand piano indicates readily how ineffective
is the function of the pin as a clamp. It can not effectively transfer the
supposed lifting motion of the string that you and others claim exists, which, in
fact, does not exist, at least from my point of view. There must necessarily be
an asymmetry of effect as the efficiency of lifting of the strings cannot
possibly be as great as that which exists when the strings are pushing down on
the bridge. Such asymmetry must result in a clipping of the harmonic motion
imposed on the bridge by the string, which you and others, apparently, believe
exists at this point, another point of subtlety, and a "troublesome question"
which appears to be disregarded, along with numerous others by your camp.
In point of fact, I have a number of books on the subject of vibrations
and other pertinent subjects and have quoted from them when requested to do so.
The quotes, their implications and other points I have made, you seem to have
found irrelevant and then simply disregarded, something, in the context of
intellectual enquiry, that is a mystery to me.
> This entire controversy boils down to a few simple questions: Are the
> motions, if any, at the bridge, the direct result of the string driving the
> bridge and thence the board in the fashion of, as you have said, a spring on
> spring system? If so, this would indeed be fantastic. AND is the motion, if
> any, of the bridge linearly related to the motion of the string? That is, does
> a very slight excusion of the string result in a very slight bodily
> displacement of the bridge, and a somewhat greater excursion result in a
> somewhat greater excursion and so on? Are these motions proportional? If not,
> then the pertinence of the example of the floating of valves in an engine is
> plain. It is simply not enough to say that something lags the other by a
> "computable phase angle" as this does not address what actually happens as that
> lag develops.
I say any motions of string and bridge are not directly functions of each
other as the strings cannot move the bridge for numerous reasons in a way
sufficient to achieve what it is you and your coproponents claim to occur and
that the stress transduction method I have described is a much better model for
this and that this model also accounts for events occuring when a tuning fork is
applied to bridge or board. Standing waves developing in the board account for
motion of the board and bridge, they are the consequence of strain energy being
pulsed into the bridge and board by the flexing string.
Why is it so hard to believe that a string, when stretched by the standing
waves occuring upon it, will pulse a longitudinal wave faithfully rendering the
periods of the standing waves across the terminations and that this will refract
into the medium in contact with the string and then diffuse through this medium,
developing through reflection and refraction imperfect longitudinal standing
waves which can then move, in the case of the soundboard, the bridge, if
necessary? This is a far simpler, at least mathematically speaking,
explanation than what you propose, notwithstanding, its evident conventional
standing.
To continue the wave analysis using your model. : Say the string is at the
unstable equilibrium configuration of the fundamental. By the "Cyclic Pressure"
method ( to take recourse to new terminology per your request) when the string is
displaced above the bridge it is pulling upward on the bridge and soundboard.
This will occur for less than half of a period, as it must proceed through the
entire gamut of free resonances: the string will then cycle to the other phase,
pulling downard again for less than half a period. In the case of A-440 it will
momentarily pull upwards for less than half the period, that is 1/880 of a
second as it must cycle through all of the other standing waves.and then proceed
to the opposite phase still cycling through the other standing waves similarly,
and all this in the other half period which is 1/880th of a second. Held down
by other strings, unable to remain effectively in contact with the bridge on the
upstroke, and attached to a massive,stiff bridge and relatively massive
soundboard, the string simply is not able to operate as a force in the manner
you defend so intently.
Regards, Robin Hufford
>
>
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