  A focused acoustic standing wave creates a Hookean potential well for a small
sphere and can levitate it stably against gravity. Exposing the trapped sphere
to a second transverse traveling sound wave imposes an additional acoustical
force that drives the sphere away from its mechanical equilibrium. The driving
force is shaped by interference between the standing trapping wave and the
traveling driving. If, furthermore, the traveling wave is detuned from the
standing wave, the driving force oscillates at the difference frequency. Far
from behaving like a textbook driven harmonic oscillator, however, the
wave-driven harmonic oscillator instead exhibits a remarkably rich variety of
dynamical behaviors arising from the spatial dependence of the driving force.
These include oscillations at both harmonics and subharmonics of the driving
frequency, period-doubling routes to chaos and Fibonacci cascades. This model
system therefore illustrates opportunities for dynamic acoustical manipulation
based on spectral control of the sound field, rather than spatial control.
