Anders Askenfelt On Pianos

[Ron Nossaman]

>       Those that have complete faith and make a religion of the view that 
>the board
>drives the piano, linearly, that is at identical frequencies as the standing 
>waves on
>the string,  and causes a flexing motion of the bridge which directly 
>imposes upon the
>soundboard these frequencies should test their generalized theories of  
>linearity by
>going out and revving up the engines in their Mercedes and Jaguars, holding 
>the RPM up
>high enough and observing the results.  A four or five thousand dollar 
>repair bill will
>likely be far more persuasive than anything I could have to say.
>     Incidentally, I don't believe that I have implied or said anything 
>relative to the
>proponents of the contrary view of the nature as suggested by you below.  
>Nor would I.
>In fact, I have been  insistent in urging civilty in this controversy as I 
>know emotions
>are necessarily attached to these opinions.


Again, find a book that actually deals with forced vibrations with harmonic
excitation, and you will find that in the case of a driven frequency higher
than the natural harmonic frequency of the system, displacement will lag
behind the impressed force by a computable phase angle between 0° and 180°.
The amplitude of movement is greatest if driven at the natural harmonic
frequency, and diminishes (but does not disappear) as the frequency rises.
That's specifically from Vibration Theory and Applications, by William T.
Tompkins, but I found something similar in at least a couple more, and a
web page or two as well. The floating of valves in an automobile engine is
an excellent example of this principal. The driving force is beyond the
resonant frequency of the system - the springs can't move the valve mass
back quickly enough to seat the valves before the cam comes back around to
lift them again. The frequency of the system is unaffected, as should be
obvious. The valve is still lifted by the cam in exact relationship to the
RPM of the engine. If it weren't, you would soon be sweeping up scattered
parts. It is the amplitude of the valve movement (specifically, the
recovery) that is affected. In the  engine, the movement in one direction
is by direct force with a spring return, and in a piano the force is spring
applied in both directions. The amplitude diminishment from driving beyond
resonant frequency is common to both systems. This has already been
addressed, and is covered quite well by "conventional" thinking and physics. 

How do you feel this specifically supports your position that the string
does not directly move the bridge? 


>     As to the question of whether my view is right or wrong, in the context 
>of  this
>discussion,.this is, as I have said, of no consequence to me.  I simply 
>prefer to
>understand the facts and their implications as they are.  Were my view 
>incorrect, then I
>would prefer to be brought to understand that by recourse to facts and
reasoned
>commentary, something in poor supply heretofore; an involuntary change of 
>view would
>then ensue.  However, loud shouting, petty inuendo, patronizing lectures as 
>to the
>nature of science  and the outraged  insistence upon the sanctity and 
>inviolabilty of
>one's view, however buttressed by others opinions,  cannot successfully 
>masquerade
>itself, to me at least, as reasoned argument.  The invigorating and 
>instructive aspect
>of this discussion  which by its clarification of ideas and analysis, should 
>lead to a
>better understanding, has only strengthened my belief that  the model of
>soundboard/bridge behavior propounded by the Ripple Theorists, a term to 
>which I would
>also happily claim credit for although it did not originate with me,  is
wrong.
>Regards, Robin Hufford

As long as you are condoning civility here, I'd prefer you drop this
"Ripple Theorists" label too, if you would. It is misrepresentative of the
point of contention here as to whether or not the strings move the
soundboard, and is accordingly presumed to be antagonistic. Note also that
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, not by invoking names of presumed authorities, with the
acknowledged exception of Isaac Newton. All you have ever had to do to
explain and justify your theory is to do likewise. I would still like to
see any logically and rationally connecting series of accepted or
verifiable scientific principals that will account for your claim.
Something specific that directly relates to your theory would be a helpful
start.


Ron N