I found this information while looking for sleep gadgets.
A very very small study (like 6 people) showed that if pink noise was played for the person right before they entered deep sleep they stayed in deep sleep longer. First, this is a tiny study so no way to know if it works for everyone, but it is easy for you to test yourself. Second, be aware that REM sleep is more critical than deep sleep, but my curiosity was if the noise would relax me more so I woudl fall asleep sooner.
White noise is supposed to match rain.
Pink noise is supposed to match a waterfall (some heavy, some light - at the same time so contrasting)
Brown noise - to me this is more like a babbling brook. I didn't read them but apparently it helps students be relaxed and study better.
There is blue and violet noise also, but there was no discussion about the value of those, however I was focused on sleep improvement.
The pink noise doesn't relax me (it actually does the opposite) but the brown noise is very relaxing for me. I found an app and will play with using this at night (part of my get ready to sleep.
You can check out the sounds with the links below (just a random sample)
NOTE: Play with your volume as it can sound different louder and quieter.
White noise: www.youtube.com/
Another white noise: www.youtube.com/
White noise that sounds more like rain: www.youtube.com/
Pink Noise: www.youtube.com/
Another Pink Noise a little quieter: www.youtube.com/
Pink Noise using deeper tones: www.youtube.com/
Brown noise: www.youtube.com/
More brown noise: www.youtube.com/
Much lower tones brown noise: www.youtube.com/
I found an app for my phone that will actually play several different "color" noises and allow me to change the volume, the base (lower/deeper sounds) and the treble (higher sounds) on them.