Much of what is currently written about brainwave entrainment, especially on the internet, is simply … incorrect.  It seems par for the course that when something of huge value is discovered as a potential ‘internet product’ that it is going to be marketed within an inch of it’s life. And often with less than stellar regard for actual science, research, or factual knowledge. 
The Alpha waves have for years been the most popular frequencies to use during Brainwave Entrainment. They have the ability to enhance light relaxation as well as positive thinking and they are often utilized for enhancing what is known as ‘super learning ability’. The Beta waves have a frequency of 13-25 Hz and they assist in enhancing a standard state of alertness. In addition, they are an effective remedy for both stress and anxiety.
Most wisdom traditions have employed methods that allow the subjects' brain waves to slow down such as meditation, [Hindu] kirtan, [Gregorian, Menzuma or Sufi] chanting, Hebrew davening, Native American drum circles and rain chants, Tibetan prayer bowls, and whirling dervishes and African trance dancing. The rhythm of these wisdom tradition technologies actually slows people's brain waves from their normal busy brain frequency we call Beta (13-30 cycles per second or Hz), to Alpha (8-13Hz) -- meditation, Theta (4-8Hz) -- deep relaxation and dreaming, and Delta (.5-4Hz) -- slow wave or dreamless sleep.
Entrainment is a physics principle in which one rhythmic system falls in synchrony with another rhythmic system. If you’ve ever found yourself moving your body to the beat of your favorite song, then you’ve experienced entrainment in its most basic form. Besides music, this principle can be found all around you, probably more than you realize. Here are a few examples:
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Subsequently, the term 'entrainment' has been used to describe a shared tendency of many physical and biological systems to synchronize their periodicity and rhythm through interaction. This tendency has been identified as specifically pertinent to the study of sound and music generally, and acoustic rhythms specifically. The most ubiquitous and familiar examples of neuromotor entrainment to acoustic stimuli is observable in spontaneous foot or finger tapping to the rhythmic beat of a song.