Sound waves(The behavior of soundboards)

[Phillip L Ford]

Date: Wed, 30 Jan 2002 22:01:33 -0800
From: Robin Hufford <hufford1@airmail.net>
Subject: Re: Sound waves(The behavior of soundboards)
 
    You misconstrue my assertions in regard to motion as I have not maintained that is
> does not occur.  Rather,  I say that substantial motion at the string bridge interface
> induced as a result of the bridge attempting to follow the so called cyclic loading of
> the board by the string during its excursion is detrimental to the sound as it will
> displace the node and thereby confuse the frequencies produced by the system.  The
> actual motion of the bridge is elastically  induced through the development of standing
> waves in the bridge/soundboard and, depending upon the particular piano, may be
> substantial or otherwise.  These are two different matters.  I maintain that the
> "cyclic pressure" proponents mistake one for the other.

>The Cyclic Pressurists belive that the flexing string lifts, pushes and pulls upon
>the bridge as a result of a force produced  during the excursion they take the standing
>waves to be.  They have been repeatedly explicit on this point, indeed, posting just
>today declarations as to these operations and, in particular, contending again the
>irrelevance of loading.

I believe this is all restating what can be summarized as - which moves first, the
bridge or the soundboard.  This has been a point of contention from the start of this
discussion.  One the one side, as you say, is the camp that says the string moves up
and down (and all around, but for purposes of this discussion let's say up and down),
which causes an up and down force on the bridge which causes the bridge to move
up and down in response (albeit with a phase lag at certain frequencies) which is
moving the soundboard up and down since the bridge is attached to it.  Or to put it
more simply, the bridge moves first and the soundboard follows.   I don't think that
anyone has tried to deny that this is the point of view of camp one.

Now camp two (that's you, and anyone else who is camping with you - I haven't
heard anyone speaking up) I believe, if I understand correctly, holds that the
soundboard moves first and the bridge follows.  The actual mechanism of this is
not completely clear to me.  I'll try to summarize what I think I have gathered.
The standing wave on the string is causing longitudinal waves (should I be saying
waves or force here?) which transfer to the bridge (which is sitting still, because
it is at a node) which transfer to the soundboard which cause standing waves to be
set up in the soundboard which causes the soundboard to move which then causes
the bridge to move because it is attached to the soundboard.  Is this a fair summary?
If not, please correct or add as you see fit.

You have repeatedly said that it is hard to imagine or believe (am I using the right
words here?) that a force can cycle at say 440 hz and that the bridge could possibly
follow.  I'm not sure why this is harder to believe than to believe that longitudinal
waves are flowing in and out of the bridge at 440 hz and causing something to happen
in the soundboard which is then moving the bridge.  Or for that matter, harder to imagine
than the string itself moving up and down at 440 hz.  All seem equally fantastic to me.
But as Faraday said:
“All this is a dream.  Still, examine it by a few experiments.  Nothing is
too wonderful to be true, if it be consistent with the laws of nature, and
in such things as these, experiment is the best test of such consistency.”

So, I would like your comment on an experiment.  Let's eliminate the string for the
moment.  Take a plunger or rod and fasten it to the top of the bridge.  Move it up
and down at 440 hz or whatever frequency you choose.  In your opinion, consistent
with your view of the way the system works, what should happen?  If I understand
you correctly the bridge shouldn't move in response to the force since the bridge
doesn't have the ability to follow a force moving up and down at 440 hz.  Since there
are no longitudinal waves being introduced into the bridge then the soundboard
should have no standing waves set up in it and thus would not itself move or move
the bridge.  There should be a couple of observable results of this.  The bridge should
have no observable motion.  No sound should be emitted.  If some movement should
inadvertently occur or some sound should inadvertently be emitted it should not be
at 440 hz since ' displace the node and thereby confuse the frequencies produced by the system'.

Would you agree with this assessment?  If not please comment or correct as necessary.

I believe the view of camp one would be that the result of this experiment would be
an observable and measurable deflection of the bridge in the vicinity of the plunger.
A tone of 440 hz would also be emitted by the soundboard.

By the way, the choice of test frequency raises another question.  You have talked
before about the nature of loading.  I've never been completely clear on this but
I have taken this to mean that the system will respond differently to dynamic
loading than to static loading.  I believe that you are in agreement that if you
displace the string or apply a load at the top of the bridge statically then the bridge
and board will deflect, are you not?  At what point does the bridge and board stop
behaving in this fashion?  1 hz? 10? 1000?  This would influence the choice of
frequency for the test.

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