That would be ideal. Unfortunately the boundary conditions are wrong. Since each end of the arrow is free, you get anti-nodes at the ends, just like in open air columns:
and nodes from the second harmonic (which dominate the motion) at about a quarter of the length in from the ends.
There is some black magic/hard engineering that goes into matching arrow stiffness and length against tip weight and bow strength to produce optimally timed and placed vibrations, but I've never dug deeply into it.
Not likely. The flex of an arrow is probably not quite symmetrical due to the weight of the point. As mentioned, the point wobbles less than the nock end. You can do things adjust the flexing.
Modern recurve archers generally spend time "tuning" their setup. You can change arrow stiffness (spine), point weight (heavier gives a "softer" arrow, lighter gives a "stiffer" arrow), plunger offset and plunger spring stiffness. Arrow length is generally fixed if you are using a clicker.
There's also some leeway with poundage. You can screw the limb bolts in or out to increase or decrease the poundage. And if you have money, buy X10s or ACEs. They have barreled shafts and in my experience are easier to tune.
Barebow archers (like the guy in the video) have far fewer variables and I think they just measure shafts to get the right tune. I've seen some go through a lot of shafts to get usable arrows.
He very specifically tests all his arrows for how much they flex, and if it's outside his tolerance, he doesn't use it (as explained in the video). In this way, he is able to normalize the deflection of the arrows he uses, and correctly predict the deflection offset.
Are the ends of the arrow free, though? It's moving through the air fast enough that I'd imagine there'd be lift/drag effects if it's not head-on to the airstream.
http://ks.kumu.net/Units/Waves/Sound/WebPages/Content_Harmon...
and nodes from the second harmonic (which dominate the motion) at about a quarter of the length in from the ends.
There is some black magic/hard engineering that goes into matching arrow stiffness and length against tip weight and bow strength to produce optimally timed and placed vibrations, but I've never dug deeply into it.