Many people experienced in using alpha brainwave entrainment report that the state of mind associated with alpha waves is a time when they feel most consciously connected to their subconscious mind. The intense experience of hypnagogic sleep, reported by some people as a feeling of being awake and asleep at the same time, is also associated with alpha brainwaves.
^ Trost W. and Vuilleumier P., Rhythmic entrainment as a mechanism for emotion induction by music: a neurophysiological perspective. In The Emotional Power of Music: Multidisciplinary Perspectives on Musical Arousal, Expression, and Social Control, Cochrane T., Fantini B., and Scherer K. R., (Eds.), Oxford, UK: Oxford University Press; 2013, pp213–225.
The phenomena of brainwave entrainment was first described in the scientific literature in 1973 by Gerald Oster in results published in an article in Scientific American entitled, “Auditory Beats in the Brain”. He showed that a specific brainwave could be induced when a person heard two separate, but closely related, sound frequencies, one in each ear. He discovered that when the frequencies heard by each ear differed by about 10 hertz, the brainwave pattern of the person hearing the sound would synchronize to the difference between the two frequencies. For example, if the person heard a 410 hertz sound in one ear and a 400 hertz sound in the other ear, their brainwaves would stabilize at the difference between the two, or 10 hertz. This technique is called binaural beats, and it is a fundamental principle of brainwave entrainment methods.
, that is, the average of the two frequencies. It can be noted that every second burst in the modulation pattern is inverted. Each peak is replaced by a trough and vice versa. However, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. Therefore, subjectively, the frequency of the envelope seems to have twice the frequency of the modulating cosine, which means the audible beat frequency is:[5]
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.

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.
With almost 100 years of research validating the effectiveness of brainwave entrainment, it’s no wonder why it’s used by thousands of people all over the world. What does the future entail in this exciting field? With the adoption of smartphones, virtual and augmented reality, and advancements in technology reducing the cost of EEG and other forms of biofeedback devices, the entrainment possibilities are endless.
15. Melville GW, Chang D, Colagiuri B, Marshall PW, Cheema BC. Fifteen minutes of chair-based yoga postures or guided meditation performed in the office can elicit a relaxation response. Evid Based Complement Alternat Med [Internet]. 2012 [cited 2012 June 27]; Available from: doi:10.1155/2012/501986.

You know how movie characters always look themselves in the restroom mirror when faced with a tough situation? Well, giving yourself a quick pep talk in the looking glass can actually help relieve stress. “‘Mirror work‘ is done by looking in a mirror and vocally speaking positive affirmations to yourself with affectionate conviction, to release worry or to improve your self-confidence,” Whitaker says. To relieve stress in the moment, she suggests using a restroom mirror, your car’s rear-view mirror, or even a compact. “Calm your mind by saying encouraging affirmations aloud to yourself, such as, ‘I am excellent at what I do,’ ‘I’ve got this! I am amazing,’ ‘I am an asset to this company,’ or ‘I am awesome!’” she says.

Delta (3hz – 0.2hz) – Deep, dreamless sleep. Intuition. Empathy. Brainwave expert Judith Pennington calls it the doorway to Universal Consciousness and “A radar that scans the environment and psychically picks up information and energy.” According to British physicist C. Maxwell Cade “There have been reports that delta waves appear at the onset of paranormal phenomena.” (More information can be found in Cade’s book The Awakened Mind)

Entrainment is a term originally derived from complex systems theory, and denotes the way that two or more independent, autonomous oscillators with differing rhythms or frequencies, when situated in a context and at a proximity where they can interact for long enough, influence each other mutually, to a degree dependent on coupling force, such that they adjust until both oscillate with the same frequency. Examples include the mechanical entrainment or cyclic synchronization of two electric clothes dryers placed in close proximity, and the biological entrainment evident in the synchronized illumination of fireflies.[13]