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.
Ahhh, so the master archer (such as the guy we see in the video) likely knows where these nodes are and can compensate his aim for that?
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.