That is generally where the science ends and the pseudoscience begins. A number of companies and individuals have then extrapolated from the phenomenon of entrainment to claim that altering the brain waves changes the actual functioning of the brain. There is no theoretical or empirical basis for this, however. Entrainment is a temporary effect on the synchronization of neuronal firing – it does not improve or increase brain functioning, it does not change the hardwiring, nor does it cure any neurological disorder. There is no compelling evidence for any effect beyond the period of entrainment itself.
So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.

The use of brainwave entrainment techniques offers many benefits for overall health and well-being, including improved emotional stability, increased cognitive function, and a deepening of creative insight. Much of this benefit derives from the hemispheric synchronization occurring as a result of entrained brainwaves. This effect happens when the electrical impulses in both hemispheres synchronized to the same frequency being delivered through the entrainment source.
In 1984 medical researcher Dr. Gene W. Brockopp published a paper making several conclusions of audio and visual entrainment (AVE). Such conclusions were that hemispheric synchronization caused by AVE is related to increased intellectual functioning, practiced use of AVE overtime leads to a cumulative effect, and AVE may result in the recovery of early childhood experiences.
Sound and light are the most popular methods to entrain the mind, yet there are a few other options in our toolbox. Using vibrational energy from sources such as magnets and electricity has been proven to help overcome addictions, depression, and even treat neurological disorders such as Parkinson’s. In this section, we cover these alternative forms of brainwave entrainment.
Social interaction is your body’s most evolved and surefire strategy for regulating the nervous system. Talking face-to-face with a relaxed and caring listener can help you quickly calm down and release tension. Although you can’€™t always have a pal to lean on in the middle of a stressful situation, maintaining a network of close relationships is vital for your mental health. Between sensory-based stress relief and good listeners, you’ll have your bases covered.
Brainwave entrainment also happens with the use of pulsating light, and visual and auditory stimuli are sometimes combined for additional effect and visual stimuli is used alone. Using brainwave entrainment techniques is safe for almost everyone, the exception being pregnant women and people who have seizure disorders who should check with their physician before using these methods.
Over the long term, traditional eastern methods (such as meditation and yoga) train your brainwaves into balance. Of the newer methods, brainwave entrainment is an easy, low-cost method to temporarily alter your brainwave state. If you are trying to solve a particular difficulty or fine-tune your brainwave function, state-of-the-art brain training methods like neurofeedback and pEMF deliver targeted, quick, and lasting results.  
The activity of neurons generate electric currents; and the synchronous action of neural ensembles in the cerebral cortex, comprising large numbers of neurons, produce macroscopic oscillations. These phenomena can be monitored and graphically documented by an electroencephalogram (EEG). The electroencephalographic representations of those oscillations are typically denoted by the term 'brainwaves' in common parlance.[4][5]