soundboard vs string

[Ron Nossaman]

>That
>being said, the visualization becomes much more complicated, because the
>extra degree of freedom in 2-D allows greater variety in fundamental mode
>geometry. It is still exactly the same in principle though. [The
>compression (longitundinal) waves are there, like on the string, but not
>part of the main function of a properly designed soundboard.] 

And here we are yet again right back at the very beginning with what I
think is an erroneous assumption. This explanation leaves out altogether
the transverse wave of the string. Take a bus to a third world country
where they still have such things and locate a clothesline. Perhaps the
very one that was used for the blanket example of soundboard waves.
Position yourself such that you can sight along one of the wires, and whack
the wire with a stick. You can see, not measure, not theorize, but see a
transverse wave travel from the point of impact to the far "T" support,
then reflect back in your direction. This is not a compression wave. This
is a transverse wave. It travels just like the transverse wave demonstrated
by the animations presented at the url you posted, and quite distinctly
different from the compression waves demonstrated at the same site. This
wave is longitudinal in that it travels along the wire, and almost surely
has more effect on the system than the much discussed compression wave that
I still can't seem to picture forming by a transverse hammer blow to a
piano string. Perhaps that's just my shortcoming, but if there are
compression waves involved at all, I see them as being third on the list
and having the least effect on the system. This transverse wave is the same
type of wave that traveled in the blanket illustration, and in the
soundboard. The same reflection, reinforcement, cancellation, blending, and
settling into increasingly stabile transverse vibrations occurs in both the
string and by the movement of the string, the soundboard. As you said,
there is no fundamental difference between the wave forms in the strings
and in the soundboard except for another available dimension for waves to
travel in the soundboard.


>As Del says, you can do it experimentally, and this is the modal analysis
>method (or equivalent). You basically drive a board (modulo all the
>various limitations discussed here about loading vs not etc) and observe
>the mode frequencies.  The other way is to model the system itself
>mathematically (e.g. FEM analysis, or more sophisticated techniques),
>obtain real parameters from experimental observation, and calculate the
>predicted response of the board (requires sophisticated computer program,
>not beer mats). This technique, apart from being more elegant than modal
>analysis, allows the critical design-related factors, viz. a casual
>relationship between board (and other) parameters and the response. So you
>can adjust parameters and see what the effect is on the response, without
>having to make an experimental board etc. This you cannot do with modal
>analysis. The modelling approach iss the sophisticated approach. [To some
>extent modal analysis can be useful too, to calibrate your modelby 
>providing experimental data.]

Unfortunately (because I'd like to see it happen), this technique is
itself, still in the beer mat stage.


Ron N