Interesting. Many natural sounds are very similar to white noise (e.g. leaves, waterfalls, etc.). We evolved in nature so our brains might be tuned to specific sounds, that is, they have a positive psychological effect.

My father, who was also an engineer, taught me when he had a difficult problem to solve he went for a walk in the woods. The solution often just came to him by magic. I wonder if it was the walking or the "sounds"? Probably both.