  Remarkably, the interface of a fluid droplet will produce visible capillary
waves when exposed to acoustic waves. For example, a small ($\sim\! 1 \mu$L)
sessile droplet will oscillate at a low $\sim\!10^2$~Hz frequency when weakly
driven by acoustic waves at $\sim\!10^6$~Hz frequency and beyond. We measured
such a droplet's interfacial response to 6.6~MHz ultrasound to gain insight
into the energy transfer mechanism that spans these vastly different
timescales, using high-speed microscopic digital transmission holography, a
unique method to capture three-dimensional surface dynamics at nanometer space
and microsecond time resolutions. We show that low-frequency capillary waves
are driven into existence via a feedback mechanism between the acoustic
radiation pressure and the evolving shape of the fluid interface. The acoustic
pressure is distributed in the standing wave cavity of the droplet, and as the
shape of the fluid interface changes in response to the distributed pressure
present on the interface, the standing wave field also changes shape, feeding
back to produce changes in the acoustic radiation pressure distribution in the
cavity. A physical model explicitly based upon this proposed mechanism is
provided, and simulations using it were verified against direct observations of
both the microscale droplet interface dynamics from holography and internal
pressure distributions using microparticle image velocimetry. The
pressure-interface feedback model accurately predicts the vibration amplitude
threshold at which capillary waves appear, the subsequent amplitude and
frequency of the capillary waves, and the distribution of the standing wave
pressure field within the sessile droplet responsible for the capillary waves.
