From David Skolnik <davidskolnik@optonline.net>
Ric -
This was one (just one) of the reasons I was so sad at not being able
to be in Rochester. I hope Steve Birkett does make the DVD available.
You said a few things:
>the initial pulse and reflections look a bit more like a Gausian
>[sic] wave then a straight traveling wave
First, just for those who may not remember their Gauss:
>A Gaussian function (named after
><http://en.wikipedia.org/wiki//wiki/Carl_Friedrich_Gauss>Carl
>Friedrich Gauss) is a
><http://en.wikipedia.org/wiki//wiki/Function_%28mathematics%29>function
>of the form:
>f(x) = a e^{-(x-b)^2/c^2}
>
>for some <http://en.wikipedia.org/wiki//wiki/Real_number>real
>constants a > 0, b, and c.
>Gaussian functions with c2 = 2 are
><http://en.wikipedia.org/wiki//wiki/Eigenfunction>eigenfunctions of
>the <http://en.wikipedia.org/wiki//wiki/Fourier_transform>Fourier
>transform. This means that the Fourier transform of a Gaussian
>function is not only another Gaussian function but a
><http://en.wikipedia.org/wiki//wiki/Scalar_%28mathematics%29>scalar
>multiple of the function whose Fourier transform was taken.
>Gaussian functions are among those functions that are
><http://en.wikipedia.org/wiki//wiki/Elementary_function_%28differential_algebra%29>elementary
>but lack elementary antiderivatives.
(quoted from Wikipedia)
Oh, that's right. Now I remember. Okay then, well, if it's Gauss
we're talking about, then, to quote Samuel Jackson in Pulp Fiction,
"Please, allow me to retort".
What??
or, to paraphrase another quote from the same source; "What does a
Gaussian wave look like?"
Anybody starts throwing Gauss around on this list better be willing
to simplify it for us morons, even if that's only a couple. (Smiley
faces not operational) Honestly though, it may have to wait until
Birkett or someone else writes "Elementary Gauss for Piano
Technicians", but until then, maybe you could elaborate and
simplify, all at once.
You also paraphrased Birkett along the lines of "namely that if you
can't measure it or photograph it...". Well, I've been wondering
about something for quite some time, but haven't known exactly how to
pursue it, though the information is probably right under my nose,
(as in previously discussed on this list). How does wire look (and
act), molecularly, at rest, and how does that molecular structure and
behavior change as tension is applied, and as it approaches and
attains breaking point? On what level does the behavior of the wire
change as a response to material imperfections (in fact, how uniform
is the molecular structure of piano wire?brand to brand?) or to
physical distortions (bend / crimp) or to the physical process of
termination? Did Birkett speak of making any observations along these lines?
Lastly, I'm not sure what you mean by:
> I am wondering at this point whether or not the <<definition>> or
> focus of the termination at the bridge is what is at work here.
Sorry to have missed you on your trip to the states, and I hope the
cinematic references were not too obscure (or too obvious) for
you. Any of you.
David Skolnik
At 05:30 AM 8/13/2006, you wrote:
>Hi Tim, Cy and John.
>
>Interesting we have already what looks to be 3 different
>interpretations of what is happening to the pulse. Seems clear to
>me that the reflection would be influenced by the whatever angles
>are involved in the clamp. I did a kind of macro experiment a while
>back with a rope terminated different ways and the effect was pretty
>clear. A slanted pin caused the pulse to be deflected differently
>then either a purely horizontal or vertical. You could see an
>initial sideways jerk as the pulse repelled from the slanted
>pin. Perhaps this causes some degree of loss ?
>
>The high speed photography that Dr. Birkett took was quite revealing
>indeed. I only got to look at a couple things he did the first two
>nites of the convention. One seires done with Tim, and another
>single experiement I helped with on a standard configured
>piano. Some of the thoughts I've been having about what happens to
>the initial pulse in general seemed supported. For one thing the
>initial pulse and reflections look a bit more like a Gausian wave
>then a straight traveling wave. I didnt get to see a side by side
>comparison of a wapin vs a standard bridge pin... and no doubt one
>would have to study closely for some time to start drawing any
>conclusions... but Birketts take on these kinds of discussions is
>something I like immensely... namely that if you cant measure it or
>photograph it... then there isnt a lot of reason to start making
>sweeping declarations about how a thing functions.
>Anyways.. back to wapin ... I am wondering at this point whether or
>not the <<definition>> or focus of the termination at the bridge is
>what is at work here. A clearer focused pulse reflection could
>result in less loss and more returned energy for the string... ?
>It was an interesting afternoon and evening I spent with Tim and Dr.
>Birkett in Rochester thats for sure. Thanks to the both of them for
>allowing me some hands on time in a bit of what both do.
>
>Cheers
>RicB