[impedance and empericism]

[Marc Damashek]

"Richard Moody" <remoody@midstatesd.net> wrote:
...
> OK numbers to the nearest whole place then.
> As the son of an electrical engineer, I have always wondered what concept
> "impedance" was supposed to convey when used as "soundboard impedance".  He
> tried his best to show me how electrical impedance was measured and used in
> formulas. So you can see why I have always been expecting formulas for
sound
> board impedance.   So not even knowing what the concept is, How can I 
think
> of a better term.
>       There is that school of science that says in effect, if it can't be
> measured, you don't know what you are talking about.   I think they really
> say if it can't be measured it can't be defined, which is the same as
> existance for them.  This I think came out of the arguments for and against
> the concept of "the ether", the hypothetical medium for electromatic
> radiation like air is for sound.
> So a perfect problem for the "emperical" (measuring) scientists would be,
> "does humidity affect frequency of tones, or any part of the frequency of
> tones?"
> ---ric


The best reference for basic formulas (not soundboard design) these days is
probably "The Physics of Musical Instruments" by Fletcher and Rossing (see
Amazon.com, for instance). It's not easy, but it's full of specific, accurate
information.

Soundboard impedance is not a single number that applies to the board as a
whole. It refers to the ratio of instantaneous driving force to resultant
velocity at any (every) given point, including any phase difference -- time
offset -- between the two. This is analogous to the impedance of an electrical
waveguide, the value of which depends on where it's measured along the
interior of the guide. It's very useful because it gives us a quantitative
handle on the effeciency of power transfer between dissimilar systems, and it
is often used in both electrical and mechanical systems to pick an appropriate
spot to join systems with the aim of maximizing power transfer. A qualitative
example: to efficiently extract energy (with an electrical pickup, say) from a
string's second harmonic, you would certainly not tap it at the string's
midpoint, where the second harmonic induces no motion at all -- one quarter of
the way along the string would be much better.

On a soundboard, it would be nice(!) to know in detail how the energy of
string vibrations is converted to soundboard vibrations at each and every
bridge pin. But *accurately* modeling the impedance (distribution) of an
object like a full soundboard/bridge/string system is a real bear. The trouble
is not the sheer number of strings or pins, it's that everything is coupled to
everything else, so for instance the horizontal component of one string's
vibrations affects the horizontal vibrations of its neighbors via forces
transmitted along the bridge [Scientific American article back around 1978].
Those induced vibrations then react back on the original string, etc., and
that's where the going gets tough. Coupled systems of large numbers of
oscillators are the bread and butter of solid-state physics, and there's
plenty of work to go around.

But the good news is that string-to-string coupling is a secondary effect, and
is much weaker than the direct coupling of each string to the soundboard
itself, so that to a first approximation -- which in this case means getting a
string to pitch and minimizing some aberrant beat rates through slight string
tension adjustments -- we stand a fighting chance of getting the work done and
having it sound reasonable.

Marc Damashek
Hampstead, MD

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