The noise is very important. Any kind of white noise is soothing for a baby... noise from water, car or even vacuum cleaner.. I used to generate a noise with:
You're using pink noise, right? I wish it would be less common to kind any kind of noise "white noise", as people might instinctively search for / generate actual white noise, dislike it, and abandon the concept. Pink noise is a particular kind of noise that's much nicer to listen to than white noise. I used it from time to time to block my cow-orkers off.