Dynamics of an acoustically trapped sphere in beating sound waves

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.