These are very interesting videos indeed. Some tempered commentary about what
is actually visible in these images.
The wave one sees impacting and reflecting from the bridge is the traveling
wave, induced in the string by the hammer's impact. This, in fact, is not a
disturbance directly responsible for the sound we hear, which should be easily
obvious from comtemplation of its frequency which is not at that of the tuned
string, a point I attempted to make three or four years ago. It does, however,
load the string with strain energy enabling its free vibration.
The transverse or shear wave you see traveling here has an energy density
that is a function of the transverse acceleration given to the wire by the
hammer and the elastic and inertial characteristics of the string. The sum
total of energy contained in it is vastly less than that required to move the
bridge/soundboard, even once, much less repeatedly and, particularly, at the
tuned frequency of the string.
Then where does the sound come from? The traveling wave is rapidly
distributing its energy into the string, overall, through reflection,
superposition and dispersion with the result that the string begins to be
energized in its free vibration modes. That is what we tune and hear: these
frequencies are different from those of the traveling wave. Counting the period
of the traveling in these images does not reveal the frequency of the audible
vibration. They could not possibly be identical with the traveling wave, by
definition if for no other reason. The wave you are looking for, along with
the rest of the spectrum is not directly visible as flexion of the wire but
exists as a very slight longitudinal strain of the wire which will require a
different approach photographically, to be made visible. For these to be
visualized sections of the wire itself will have to be made to stand out against
a defining background which will need to be used as a reference line. When this
is made visible one will see the vastly larger traveling wave passing, which is
visible now, for a while at least, along the modal section of the string.
So far as motion at the bridge, any functional piano has been empirically
designed to eliminate, regardless of new theories of the last 35 or so years,
which have become very fashionable, as much as possible, within certain limits,
such motion
However, stipulating for the moment that the traveling wave one sees, and I
have seen other, similar videos, provides a flexural component that moves the
bridge, an exceedingly popular concept, consider what must happen when an
adjacent unison is also sounding: Neither could possibly produce the frequency
either produced when sounding singly, an elemental, simple, basic point
misconstrued by the "modern" flexural/impedance model which is, in reality, more
appropriate to vibration analysis of machinery and not of the acoustic function
of a soundboard.
Of course, as I have many times indicated, I believe this model, however
widespread, to be completely flawed, for many reasons. One does not see a
corresponding "yank" at the bridge, even for the traveling wave, which, of
course, certainly exists and has, I believe, a far greater level of energy than
any mode of the string, because the bridge/soundboard system is strong enough to
withstand the impulse of the string without yielding significantly. This does
not mean there is not a reaction here, of course there is, and must be, however,
it, for the most part, is on a molecular level. The string is not still at its
termination because it is a node: it is still because the immobility of the
soundboard/bridge/string interaction is sufficient such that it forces a node.
This does not mean complete rididity or lack of mobility: it is a matter of
degree.
A reaction to a force need not do work, that is experience displacement,
or, in this case make itself evident as a flexural event, but does, still,
nevertheless exist. Its existence though, is as a wave disturbance traveling
through the medium. The soundboard/bridge/string/pin system is a subtle machine
which has been evolved to operate in just in this fashion: that is to acquire
the strain energy imparted to it by the hammer as a shear wave, transform it to
acoustical effect through allowing the string to vibrate in its free modes, set
by the tuner. It then pulses the sound out of the string into the soundboard,
which through superposition concentrates it in the time domain and radiates it
away at higher sound pressure levels than would otherwise be the case. This
requires a certain degree of stiffness such that the modal vibrations of the
string are not disrupted by motion at the bridge, which is called loop
stability, while at the same time taking care that stiffness at the bridge does
not compromise the vibratory capability of the board in various aspects, by
which this sound is, as mentioned, then concentrated and radiated away.
It is astonishing how widespread is the incorrect notion that the string
lacks sound. In fact, the system works to do just that: produce sound in the
string which interacts with the bridge and bridge pins as a pressure
excitation. This pressure is the sound pressure in the string at its various
components and not a change in the static, mechanical, pressure of the string
bearing on the bridge, or pulling up on a bridge agraffe.
At some level of resolution, I am sure, eventually some motion will be
detectable: this will be neither harmonic, of constant frequency, or linearly
related to either the traveling wave or the frequencies pulsed into the bridge
by the string.
The driving-point, or transfer impedance model so widespread, is, in
reality, more appropriate in vibration analysis, that is, in the analysis of
machinery and incidental vibrations and, not particularly appropriate, in my
opinion, for an acoustical approach to a piano soundboard where the critical
need for loop stability has forced evolution of the system in just such a was as
to negate many aspects, however legitimate, of this kind of analysis, in
particular, the impedance mismatch of the wave energy on the string and the
soundboard/bridge/pin effector, for lack of a better word.
In point of fact, the impedance of a real soundboard system as a whole,
once any functional panel has been built, cannot be substantially altered by the
relatively slight changes in wire dimensions advocated by users of rescaling
techniques, although there, I think, are other reasons to do so, by changing the
rib profile, or by changing the bridge dimensions, as is routinely assumed to be
the case.
This is so because the impedance mismatch between the soundboard component
and the acoustic activity on the wire, including also the traveling wave, has
already been made so great that slight tweaks like these are, essentially,
trying to empty a thousand gallon bathtub with a teaspoon: It takes a great
deal of change to make a difference, or be noticeable.
Even though I believe the Five Lectures, are, in fact, merely a rudimentary
beginning in the proper analysis of soundboard behavior, and have said so here,
one should take to heart the implications of the testing which one of the
articles reports: measurements taken of the soundboard output with ribs on the
board taken as a measure of the transfer impedance of the system. These ribs
are then thinned, additional measurements are then taken with no difference
measurable in impedance. Additional thinnings and measurements continue until
a rib is completely planed away, yet: no difference. At the moment I forget
which article this is but would urge any wishing to understand this phenomenon
to find the Lectures, familiarize themselves with this particular study, and
contemplate the reason why. This is but one of the troublesome questions I
alluded to years ago.
Regards, Robin Hufford
courseery very amazing videos! But I notice two things. First, (referring back
to
> my previous post), in the A#14 video I am not really aware of ever seeing a
> wave for the fundamental. Does one actually exist? Second, there is
> something funny going on in that you can actually see the waves on the two
> strings go out of sync (phase) with each other. String length differences?
> Slightly out unisons? Compare to the tri-chord video where the three strings
> are dead on in sync (phase) for the entire time.
>
> In any case, very amazing video. Thanks Stephen.
>
> Geoff Sykes
> Assoc. Los Angeles
>
> -----Original Message-----
> From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On Behalf
> Of Stephen Birkett
> Sent: Sunday, August 14, 2005 10:23 PM
> To: Pianotech
> Subject: Re: string termination
>
> >I don't plan to hear or measure anything. I only want to look and
> >see what is happening to the string.
>
> A commendable objective Carl.
>
> To whet the appetite a bit take a look at the high speed images I
> have on my website...some strings, dancing dampers, and bridge pins.
> These were simply taken for interest and to test out the system, and
> definitely not under controlled circumstances, so they won't answer
> the detailed carousel (aka merry-go-round to those on the other
> pond-side) of questions about strings and terminations. They do show
> the complexity of the situation and the difficulty of making causal
> generalizations. There is a plan to tackle this question as part of
> our grand scheme of things here. First we have to learn how to be
> creative with the equipment, so we can get multi-directional
> synchronized images and see what's going on in 3-D with only one
> camera. My plan is to isolate single variables that can affect string
> motion (e.g. see Ron's long list), maintaining all bar one which gets
> adjusted and the effect on the string monitored. Needless to say this
> requires a precisely repeatable key actuation so comparisons at
> successive times are meaningful, but that one we have licked already.
>
> The ftp server on my usual website is out of action at the moment, so
> best go to the mirror site I have. The high-speed stuff is at
> http://fortepianos.com/high%20speed%20imaging.htm Note carefully the
> instructions given for getting your system set up to play these. The
> compression is extreme (each video starts raw at 500MB and compressed
> to about 5MB) to make them manageable files, so you'll need to get
> the correct video codec installed if you don't already have it.
>
> Stephen
> --
> Dr Stephen Birkett
> Associate Professor
> Department of Systems Design Engineering
> University of Waterloo
> Waterloo, Ontario
> Canada N2L 3G1
>
> E3 Room 3158
> tel: 519-888-4567 Ext. 3792
> fax: 519-746-4791
> Piano Design Lab E3-3160 Ext. 7115
> mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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