The link I‘ve posted was just one of several articles I have read. They experimented with a lot of different plants and all kind of sounds and styles of music. Me too, I was expecting a positive effect with natural sounds such as wind, birds, bees, etc.. But the category nature isn‘t the key, only the sound of water had a certain influence on the roots. They put the roots of a plant in a closed, absolutely empty, like a reversed „Y“-formed, transparent test tube. One string of the reverse Y was immersed into a a bigger tub of circulating water. The plant directed its roots towards the string with the circulating water around it ... ergo: plants felt the vibes of circulating water and they certainly have still a lot of little secrets waiting to be discovered.
As I said, some plant species show a better growth/higher yield, others don‘t. But all of them had one in common: Biggest improvement was achieved by Mozart, Vivaldi and others of the Grand Masters.
I was contemplating the effects of vibrations on plant growth earlier today. I was not thinking in terms of root growth but you bring up a very interesting point here. Perhaps you could set up a situation where you place a fan just touching the outside of the planter/pot to direct root growth? There seems to be quite a bit of research out there following this vein of inquiry as well as soundwaves. Interesting stuff for sure!