Why is the sound of running water soothing? What is it about the sound of running water that soothes the brain and the soul?

This is what I found on the internet:


  Our species evolved where trees met savannahs and where freshwater
  sources were present. Our brains are deeply encoded with the love of
  water – we revel in the delicious feel and noise of burbling brooks…


and


  I personal think we LOVE the sounds of running water because inside
  the womb of our mothers, that's what we hear...along with the sounds
  of her beating heart. I was told that we hear the blood running
  through her veins in utero.
There cannot be a single answer to this question which would be entirely correct. Different theoretical approaches to psychology will yield different explanations. This is evident from the other answers in this question (some which you provided) which all stem from different theoretical accounts:


Evolutionary Psychology: Species evolving around water
Developmental Psychology: Prenatal development in womb
Sensory and Perception Psychology: White noise account
Behaviorism, specifically Classical Conditioning: We develop a learnt association between the sound of water and relaxation.
A prediction based on a cognitive science approach is less clear in my opinion. It would likely stem from a combination of sensory arguments (white noise) and from neural networks of association.


Why do we see so many different accounts for the same phenomena? Firstly, it is difficult to produce a falsifiable explanation for why such a perverse qualitative effect exists. In order for any given explanation to be scientifically valid, it has to be able to be tested. The explanations provided so far do not generate meaningful hypotheses which we can test using experimental studies. Therefore, it is difficult to form a single model accounting for why we find water sounds relaxing. Consequently, we see a range of explanations with little evidence for any of them (they are all just untested just-so stories). Note, even some of the better responses, such as this one (linked above), do not provide falsifiable or testable answers.

A second reason we see such variation could be that there is no simple answer. The "true" answer probably will draw upon a wide range of reasons for this phenomena. In this way, perhaps the best explanation at this point is that there are a variety of reasons why certain individuals find water sounds relaxing (those aforementioned). Although perhaps not the most satisfying conclusion - it is likely the most accurate.