Brain wave entrainment is a real phenomenon and is useful as one method of investigating how the brain works. But there is no evidence, nor any theoretical basis, for any long lasting effect on brain function or that there is any benefit of any kind. Despite this, there is a huge industry of devices that claim to train your brain waves and have a beneficial effect. I wouldn’t waste a dime on any such device.
Move-Thru-It Strategy: to support optimum recovery rates, use 6-8 pumps or 3-4 droppers. Repeat every 1-3 hours for a day or two (with a good night's sleep). The idea here is a persistent frequency. Once you have achieved initial results, you can switch to more conventional usage patterns such as 3-4 times a day. For example: Kick-Ass Immune, Get Over It
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Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
After fixation upon our phenomenon takes place, what started out as a random perception is now cemented into our experience of, and is conditionally associated with entrainment. We condition ourselves to relive the same experience associated with entrainment each time we use it. It isn’t random any longer. It is explicit conditioning, and it repeats as predictably as the sunrise using entrainment as its new trigger.

When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  
But the notion of changing brain waves is a very appealing one, from a marketing stand point. People can visualize brain waves and we like synchrony. Also, in the computer age, we understand the notion of “programming.” We also have been prepped for the future by movies such as The Matrix, where people could master Kung Fu in minutes by simply “downloading” the knowledge. This gives the whole notion a superficial plausibility. But the science just isn’t there.
Infra-Low brainwaves (also known as Slow Cortical Potentials), are thought to be the basic cortical rythms that underlie our higher brain functions. Very little is known about infra-low brainwaves. Their slow nature make them difficult to detect and accurately measure, so few studies have been done. They appear to take a major role in brain timing and network function. 
Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).  
Changes in neural oscillations, demonstrable through electroencephalogram (EEG) measurements, are precipitated by listening to music,[20][21][22][23][24][25] which can modulate autonomic arousal ergotropically and trophotropically, increasing and decreasing arousal respectively.[26] Musical auditory stimulation has also been demonstrated to improve immune function, facilitate relaxation, improve mood, and contribute to the alleviation of stress.[27][28][29][30][31][32][27][33] These findings have contributed to the development of neurologic music therapy, which uses music and song as an active and receptive intervention, to contribute to the treatment and management of disorders characterized by impairment to parts of the brain and central nervous system, including stroke, traumatic brain injury, Parkinson's disease, Huntington's disease, cerebral palsy, Alzheimer's disease, and autism.[34][35][36]