The Wave-Driven Oscillator: Granular Matter Levitated by Beating Sound Waves

The acoustical force landscape created by beating between interfering sound waves
can organize granular matter into fascinating and potentially useful dynamical systems.
Even a single particle levitated by two detuned sound waves exhibits
operating states ranging from sawtooth oscillations to hierarchies of period-doubling
routes to chaos intermixed with Fibonacci cascades. All of this complex behavior is captured
by a model based on a linear harmonic oscillator driven by a simple harmonic wave.
This wave-driven oscillator model can be derived from an acoustokinetic analysis of the
forces exerted by beating waves. Deceptively simple and phenomenologically rich, this
model appears not to have been discussed previously. Its predictions are borne out by
experimental observations of a particle levitated by a pair of ultrasonic transducers.