Sound waves(The behavior of soundboards)

[Phillip L Ford]

Robin,
I probably shouldn't be responding to this since I haven't really had enough
time to consider the references that you gave previously.  However, I don't
want to ignore this altogether, so I'll give some thoughts of the moment.

On Sun, 20 Jan 2002 12:24:58  
 Robin Hufford wrote:
>It is possible that a body may experience a
>change in the velocity of its particles, atoms, molcules, whatever, and yet not move
>bodily.  Increase or decrease of heat is, as I continue to point out,  an example of
>this; another is the induction of stress waves

Yes, I acknowledge this.

>      Infofar as the quote offered last week,  now submitted again and properly
>attested,  it is from Den Hartog p. 128-129;
>"If an alternating force acts on a mass of an n-degree-of freedom system, there will
>be n-1 frequencies at which the mass will stand still while the rest of the system
>vibrates."

I believe we would call the points where the mass is standing still nodes.  The fact
that there are nodes on the string doesn't indicate that the string is not in motion,
but that this particular point (or mass) is not in motion.

>      Although the statement itself is unambiguous, Den Hartog immediately qualifies
>it by urging care be taken in its application which has to do with a system in which
>a resonant frequency  approaches the "vibration absorber frequency".

Sorry, I don't know what the vibration absorber frequency is.

>  Nevertheless,
>as the string and soundboard are, essentially, systems of infinite degrees of
>freedom, then obviously, vibrations of an infinite number of frequencies may occur
>while some part of the system may stand still.  Of course, no such thing, in
>particular as regards an infinite number of frequencies, can exist, I merely urge
>the point, as I have done,  that motion of the string does not, necessarily imply
>motion of the bridge as the string termination at the bridge is a node.
>Regards, Robin Hufford
>

As you and Den Hartog point out the end of the string is a node and by theoretical
definition can have no motion.  I don't have an explanation of how this is consistent
with the idea that the string is physically moving the bridge.   However, as someone
else pointed out (and I think you agreed) if the end of the string did have a small
amount of movement it could still act effectively as a node.  You say that the motion
of the string does not necessarily imply motion of the bridge.  Others say that the
motion of the bridge must occur for the system to work.  Can you propose an
experimental means of verifying directly on a piano that motion does not occur
or that if it does it has nothing to do with sound production?

Also, I am replying to this after reading Ric B's posts on Anders Askenfelts
offerings on how the piano works.  Do you have any comments on what he said
relative to what you have said about how the soundboard system works?

Phil F


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Phillip Ford
Piano Service & Restoration
1777 Yosemite Ave - 215
San Francisco, CA  94124