Sound waves(The behavior of soundboards)

[John Delacour]

At 1:01 PM -0500 1/23/02, Charles Neuman wrote:

>Again, the model I described above is not intended to model a piano string
>exactly. But it does demonstrate that a string can have vibrational modes
>where one termination point can move.
>[....]
>P.S. I guess it's time I "came out" as having a significant physics
>background. However, that doesn't mean I'm an expert in acoustics, so I
>haven't had much to say before.

Charles,

Thanks for a very clear and informative message.  Yes, everything you 
have written makes sense, and a lot of it is covered in the Weinreich 
lecture with illustrations of three types of termination considered.

It's good to have someone with a physics background entering the 
discussion, because you may well be able to point out fallacies in my 
arguments.  If you've been following the thread, you will have seen 
that I have chosen to consider the whole question at a molecular 
level since it has seemed to me that it all has to do with forces if 
one kind or another, whether intermolecular forces or forces at 
interfaces.  The reason I have chosen to do this is that this is the 
only way I can begin to picture to myself, let alone anyone else, how 
things work.  In adopting this approach, it is possible I am 
committing a fallacy and that a mathematical model approach using 
calculus would reaveal the fallacy.  I'd be interested to hear what 
you think about this approach.

In particular, since I posted a message this morning giving a 
decription of the way a vibration passed down the bridge, do you see 
any sense in this?  You talk in your message both of the movement of 
the termination of the string (which so far as I am concerned has 
never been in doubt) but then you refer also to the movement of the 
bridge in response to the movement of the termination.  I am seeing 
this as a progression of displacements of the particles of the bridge 
or a pressure wave, as I have described in my one-dimensional 
example.  This is just part of what happens, put at its very 
simplest, of course, since by the same analogy I would see similar 
pressure waves moving in other directions, being reflected etc. not 
to speak of bending waves as well.

I ask this because someone, nothing to do with the list or pianos, 
but extremely well qualified to talk of the vibration of plates and 
an acoustics PhD has today responded to a message I sent asking about 
precisely this.

He writes:

>1) a finite structure such as the bridge, can only really be considered
>to carry waves if the wavelength is small compared to length of the
>bridge. I haven't done the calculation but I suspect the frequency where
>waves can be considered to occur in the bridge is very high.
>
>2) a bending wave passing down the bridge (if it can occur) will still
>have a rotation at the very end which will provide a moment excitation
>to the sound board.

I have not yet pondered very long on this and would welcome your 
comments.  If my view of the "movement" of the bridge is fallacious, 
how would you describe the "movement" of the bridge, say when a 
single string is sounding and vibrating in the vertical plane?

Hope you can throw some light on this.

In spite of the "interminable length" of this discussion, I have 
actually learned a great deal from it and I can hardly imagine that 
others have not had to modify their view considerably as a result of 
the thread.  When it began, there was no evidence that anyone had 
even heard of Acoustic Radiation or Bending Waves and at this stage 
in the proceedings we have discovered, it seems, that the latter is 
almost solely responsible for the former.  In a little while we may 
discover that this is a gross over-simplification of the case -- who 
knows?

At any rate I am glad to have been forced to learn so much, and will 
be equally glad to unlearn anything that I've got wrong.  I've 
learned more by mistakes in my life than by any other method.

Look forward to hearing more from you.

JD