Let's get just a tiny bit technical; the steeping phenomenon is a result of two processes that faciltate interactions within the fluid, dispersion (bulk movement of the fluids, aka mixing) and diffusion (molecular interactions). The dispersion can be accomplished several ways, including shaking bottles, using a magnetic stir plate or a rock tumbler, and putting juice in your hubcaps and driving down a bumpy road in an old pickup truck (thanks rowdyplace). Diffusion will occur by itself whether we want it to or not, but we can accelerate that process. The most accessible method is application of heat, and that can be accomplished several ways, but excess heat can be detrimental.
Limited experimentation has been performed by several ECF DIY forum members, and some helpful strategies were developed. Heat was shown to be the most significant accelerator, and anyone that has actually read Danny's blog about steeping will see that, for most intents and purposes, a crockpot or similar device that can keep the juice around 150 deg F and occasional shaking was found to be about as effective as using an ultrasonic cleaner (UC), with a good old fashioned thermos filled with hot water coming in close behind.
Is the ultrasonic action of the UC completely useless? That has not been proven one way or another, but the UC might boost the dispersion of the fluid by some tiny amount while it is in a hot water bath. Does it actually create a harmonic resonance in the fluid that greatly facilitates diffusion? Possibly not, and that is where the frequency will determine the degree to which diffusion would be accelerated. So, Ernie, you have a point, but it is only one part of the larger picture, in my opinion. Certainly a UC that can hold the juice at the right temperature will work at least as well as a crockpot that does the same thing. And could the UC also create tiny dispersion waves within the fluid, regardless of frequency, to at least some miniscule degree? I don't see why not.
But here is where the real take-home exists, as far as I can see: once you have the juice at 150 F or so, shaking it becomes much more effective, simply because the viscosity has been reduced, so the dispersion forces are more completely distributed in the fluid. Diffusion will progress relative to the concentration gradient in the fluid, and left sitting untouched at room temperature, diffusion will proceed very slowly. Adding heat and agitation at the same time (or with quick alternation) can reduce a four week steep time to a matter of hours. That has been proven many, many times.