When you hear the term sonolevitation you might start thinking of a potential method for the construction of the pyramids and then dismiss it.
After all, who at that time could produce such an intense sonowave.
So it's impossible. But then again......Su Zhao and Jorg Wallaschek wrote A standing wave acoustic levitation system for large planar objects. In this book they discuss an acoustic levitation system that can levitate planar objects that are much larger than the wavelength of the applied acoustic wave.
They observed that a sound radiator in conjunction with the levitated planar object creates a standing wave field. Although these forces are normally weak, they can become powerful when using high intensity waves due to nonlinear characteristics.
Rayleigh1 first studied nonlinear acoustics in 1902 as an acoustic counterpart of electromagnetic waves.
Reference 1 outlines the Matrix Method to simulate acoustic levitators. Using an ultrasonic transducer and reflector. See Figure 1.
A schematic of the matrix method (Image courtesy of Reference 1)
Scientists at Argonne National Labs used this technique in 2012. Check out this video. The University of Tokyo, Nagoya Institute of Technology has a good overview of Three-Dimensional Mid-Air Acoustic Manipulation from 2013.