> An ideal string, being perfectly limp (i.e., having no "beam stiffnes") can
> form a perfect hinge at each end. Every real string, because of its
> stiffness, must deform with a short length of reverse curve at each end,
> moving the point of inflection away from the end, and causing the frequency
> to be higher than that of an ideal string of the same length.So, "It is as
> though the string is shorter".

I appreciate your point and your explanation.  A shortened effective 
length is indeed an aspect of a semi-rigid string.

However, there are other aspects (eg, the restoring force from 
stiffness) whose relative importance we have not ascertained.



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