Obviously it has to taper from the fixed end to the most mobile one. Or from the centre (node) of a symmetrical one to the ends (antinodes). Talking about longatudinal harmonic resonance only here. Ideally the static instants at full compression or tension would give a constant percentage length change from unloaded along the rod. Does it follow that at any giventime, a point X distance from the node, has Velocity and acceleration: both proportional to X or am I confused? I'm pretty sure this is an integration of shm mass/spring systems or somesuch. Is there a formula that emerges for the rate of taper of the crossectional area for a given material elastic modulus and frequency?