White noise is a random pattern of sounds within a given frequency range. The term is used in many electronic and acoustical situations. Usually the term refers to a combination of all frequencies that a human can normally hear. The result is like a waterfall in sound. Systems engineers and mathematicians have methods to deconstruct and classify different kinds of white sounds (e.g. Gaussian, Cauchy, etc.)
One use of white noise is in masking other sounds. Sounds that may be irritable or troubling can be "drowned out" by all the other noise in the white noise. This may be why white noise helps induce sleep - by removing from the brains attention what might cause arousal.
Noise loud or unusual enough to be noticeable can make it difficult to sleep, and can wake you up or make sleep more fragmented. White noise smoothes the aural environment. Resistance to noise seems to be a sign of sleep depth and of brain activity during Stage 2 sleep. The presence or absence of artificial white noise does not seem to affect sleep architecture or learning.
Even before modern times people often sought places with ambient white noise to sleep. Proximity to the babbling brook or windblown orchard helped people sleep. Such unintended random noise generators such as fans, humidifiers, and running toilets also help people sleep, although this is a touchy subject and what soothes some people can be irritating to others.
With the development of radio and television it became easy to generate something like white noise. Setting the radio to a frequency with no local station generated static, and in the early decades of television, stations went off the air overnight. Today's computers and related devices allow other ways for sleepers to generate white noise. Programmers have developed white noise generator applications for mobile phones or computers. Strictly speaking, these are sometimes "pink noise" generators - they cut off the high frequency elements that can be disturbing or irritating. Pink noise appears to be more conducive to sleep for a wider range of the population.
Pink noise is similar randomness but in which higher frequencies have less spectral power than lower frequencies. While in true white noise, all frequencies have equal power spectral density, resulting in more energy in the higher frequencies, pink noise sets the power density inversely proportional to the frequency.
Some argue (we cannot find scientific evidence) that pink noise is more conducive to sleeping that white noise.
Brown noise takes this concept to the next level, further dampening noise at higher frequencies to produce an even deeper, richer sound.
Think of a roaring waterfall or evenly crashing ocean waves.
The brown note, also known as the disco dump, is a subsonic frequency around 9 Hertz (Hz) that supposedly rocks so hard, it causes people to lose control of their bowels. Conspiracy theories about this nauseating tone go back to before World War II, and some people believe government forces belt out inaudible brown notes to disable unsuspecting audiences.
In any case, all these noises are available for free or little money on the internet. With an internet connection and a little work you should be able to set up a noise generator near your bed. Try different noises or frequencies and record your sleep in a sleep diary to find out what works for you.