I doubt if the resonance frequency of the material itself really matters. The rod or tube is touching the wood at multiple spots along its length, breaking it up into a complex system.
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Putting graphite rods in a neck doesn't affect your ability to adjust it at all. It may make it less necessary, but the truss rods in all my "hot rodded" graphite rod reinforced necks work just fine.
Of course it does affect it ... if you have a stiffer neck, it's harder for your truss rod to do it's job. If you had an infinitely stiff neck, no truss rod would be able to adjust it.
The truss rod is there to counteract the forces of the strings. With a stiffer neck, as the neck counteracts more of the string tension itself, the truss rod has to do LESS work - it's not harder for the truss rod to do its thing, it's easier. My "hot rod" necks never need more than a half turn on the truss rod from slack, and I like a very straight (.006" relief) neck.
... which goes back to my point previously ... you lose some ability to adjust your string height with the truss rod on reinforced necks.
I'm of the camp that you NEED that adjustability, because the instrument does 'breathe'.
Of course it does affect it ... if you have a stiffer neck, it's harder for your truss rod to do it's job. If you had an infinitely stiff neck, no truss rod would be able to adjust it.
I don't get the goal here. What is the point of these reinforcing rods? Someone is selling the market on the idea that stiffer necks are correlated to better tone and long term stability. I don't get that; we have lots of anecdotal evidence this is not true.