Hi, Nick.
Thanks for this explanation, the image is really helpful, and makes
intuitive sense to me.
However, as has been repeated here previously, Dr. Sanderson has said
that (if I understand him) inharmonicity is due to the material's
stiffness at the attachment points only, and that mass at the
non-terminal nodes is not a factor. Whereas, your knot analogy/image, if
I understand it correctly, says that mass at the node _is_ to be
subtracted from the mass of the segment. So is Dr. Sanderson just wrong,
or is there some way in which you're both right, that I'm just not
getting? Can you clarify? Thanks.
-Mark Schecter
Nick Gravagne wrote:
> Hi Stephane,
>
> snip <
>
> So now a thought experiment.
>
> If you can imagine that all points of string segmentation (including the
> attach points, or termination points) exist as loosely tied square
> knots, then the actual and useful and “shorter” vibrating segments exist
> */between/* the knots, since these rather large knots would interfere
> with pure vibrational segmentation from point to point. As the string is
> tightened the knots also tighten allowing “longer” segments to vibrate
> unimpeded. Tighten the string still further and further until
> theoretically the knots are so tight that they are practically
> nonexistent and now all segments, including the fundamental, are
> vibrating closest to their theoretical lengths. Since these knots can
> not disappear altogether there will always be some measure of
> inharmonicity.
>
> While this analogy isn’t perfect, keeping the visual in mind helps to
> imagine that fatter wire will also have fatter knots at any tension, and
> that thin wire will always have smaller knots at any tension. Still, the
> properties of the material itself (E) primarily determine inherent
> stiffness even if higher tensions tend to smooth out and lower
> inharmonicity by allowing the many segments to vibrate closer to their
> theoretical frequencies.
>
>
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