This phenomenon is best known in acoustics or music, though it can be found in any linear system: "According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes".[2] If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant as when a pure note is played, but change over time: when the two waves are nearly 180 degrees out of phase the maxima of one wave cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the perceived volume.

The brain is composed of millions of specialized cells called neurons. Neurons send signals to other neurons using electro-chemical messengers called neuro-transmitters that attach to receiving sites located on the neurons themselves. There is a space between the end of the neuron and the receptor called the synaptic gap. As neuro-transmitter chemicals move across this gap, a small electrical charge is created. 

Brainwave entrainment through the use of binaural beats is a scientific method that helps you go from alert to relaxed to asleep within minutes by using a process to alter your brainwaves. Sounds like something straight out of a science fiction novel, but brainwave entrainment is a very real and very effective way to help you sleep. Your alertness is linked to the dominant frequency of your brainwaves. So if you’re feeling alert and focused, your brainwaves are in the beta frequency but if you’re feeling relaxed, they’re likely to be in the alpha state. To sleep, your brainwave frequency needs drop to a slow delta. This can be hard, especially after a busy day. Your brain stays alert, preventing you from relaxing. By using Binaural Beats, you can quickly induce the frequencies associated with sleep in your brain within minutes.  Scientists discovered that the brain synchronises itself to a dominant frequency. So by inducing a new lower frequency with binaural beats, your brain begins to lower its own frequency to match this new frequency. It’s a powerful technology that I’ve been using myself for years with very good results.
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)
First of all, thank you for a most remarkable achievement. I have tried products in the past that purported to synchronize meditation-level brain waves — usually overlain by sappy new-age music composed by non-composers — and was invariably disappointed. However, I have been using your Equisync II and Equisync III recordings for a few weeks now and the results are truly astonishing and live up to the claims on your website.
I like it. I like the fact that I can just sit there and observe my thoughts and feelings and then go back to watching my breathing. It really does teach me to be centered and balanced. I look forward to the next several weeks. By the way, what I am doing now is meditating for 23 minutes in the early morning and again 23 minutes in the early evening. I’ll check back with you.
In 1956, the famous neuroscientist W. Gray Walter published the results of studying thousands of test subjects using photic stimulation, showing their change in mental and emotional states. He also learned that photic stimulation not only altered brainwaves, but that these changes were occurring in areas of the brain outside of vision. In Walter’s words:
In shamanic traditions, drums have long been used to transport the shaman out of his or her body into other realms of reality through the use of constant rhythmic vibrations. Researcher Melinda Maxfield, studying the Shamanic State of Consciousness, found that the steady rhythmic beat of the drum struck 4.5 times per second was the key to transporting a shaman into the deepest part of his shamanic state of consciousness. With the invention of the EEG (electroencephalograph) Biofeedback researchers discovered that theta brain waves oscillate at 4.5 beats, or cycles, per second. In direct correlation, we see similar effects brought on by the constant and rhythmic drone of Tibetan Buddhist chants that transport the monks and even other listeners into realms of blissful meditation.

You’ve heard me talk before about how sound can make a difference to sleep. Patients often tell me that they fall asleep to relaxing music, they seem to find it really helps them let go of active thoughts and quiet their mind—which, like yours probably does, tends to race from one thing to the next all day long (aka I can’t turn off my brain syndrome).

One RCT (n=108) showed significant reduction in anxiety from a single session of alpha/delta therapy for day surgery patients. A crossover RCT of a single session of theta stimulation in four healthy adults reported significant improvement from the intervention in one of five measures. Five pre/post studies reported significant benefit from the intervention for 16 of 27 outcomes.
There has been considerable interest in the potential of auditory beat stimulation to affect cognition and mood states.  Chaieb, Wilpert, Reber, & Fell (2015) reviewed the literature on the effects of auditory beat stimulation on memory, creativity, attention, anxiety, mood, and vigilance. They found some support for it being able to affect these modalities but there were contradictory findings. So the area clearly requires significantly more research before firm conclusions can be drawn. 
The only thing I have found lacking in using your product is that there is no place on your website to register my kudos to you for such an excellent product. I am not new to meditation, nor to brain entrainment products, and I found you product to be really outstanding. I’m completely hooked, love listening to the tracks and they are the best way ever to treat monkey mind. Bada boom, bada bing, in just a few minutes any aggravation I’m experiencing in the outside world, melts away and I am one very blissful and happy camper.
Cvetkovic D, Simpson D, Cosic I (2006). “Influence of sinusoidally modulated visual stimuli at extremely low frequency range on the human EEG activity“. Conference proceedings : … Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 1: 1311 – 4. doi:10.1109

This kind of conflicting evidence regarding the effectiveness of binaural beats to produce valid and reliable changes in brain waves abounds in the literature. For example, Rosenfeld, Reinhart, & Srivastava, (1997) found that in a sample of normal college students, alpha and beta audiovisual stimulation showed evidence of brainwave entrainment, but baseline levels of alpha and beta among the participants affected the observed degree of entrainment, producing significant individual differences in response. López-Caballero & Escera (2017) found that administration of binaural beats in the various frequency bands produced no changes in EEG spectral power between the time periods of baseline and those periods with beats presented. Likewise, Wahbeh, Calabrese, Zwickey, & Zajdel (2007) found no effect on brainwaves with the administration of alpha frequency binaural beats. It is easy, however, to find personal testimonials online. 
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.
Binaural beats are an auditory illusion where two oscillators, slightly detuned from each other, are played simultaneously with one perceived by each ear. The human brain mixes the audio from each ear, and the listener perceives a "beating" effect that isn't actually there. This is a well-studied phenomenon that has gained the interest of audiologists and neurologists, but it's most famous for being picked up by the alternative medicine community as a way to get high.

... One of the possible explanation for insignificant results could be length of exposure to AVS. Our participants were exposed to it for 11 minutes, while some authors (Cruceanu & Rotarescu, 2013) suggest that at least 20 minutes is needed for the positive effects to take place. Furthermore, part of our reserach was also visualization of gymnastic skills, performed after AVS. ...

The functional role of neural oscillations is still not fully understood;[6] however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory.[7][8][9] Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.[10][11][12]

I tried other companies the last few years or so….among the likes that mainly used binaural audio and the deepest I was really ever to achieve was alpha state….maybe theta once or twice over the last few years. It takes incredible dedication and practice to achieve the deep, renewing states of meditation that are most sought after…..I listened to the theta meditation mp3 last night and within what seemed like a few minutes my mind was flooded with imagery…memories long gone…my body was sleeping, heavy as lead, but my mind was crystal clear, aware of my surroundings. I could barely even open my eyes!

“…humans have always been intrigued by the possibilities for influencing mental functioning that emerge from combining rhythmic sound and rhythmic light stimulation. Ancient rituals for entering trance states often involved both rhythmic sounds in the form of drum beats, clapping, or chanting and flickering lights produced by candles, torches, bonfires, or long lines of human bodies passing before the fire and chopping the light into mesmerizing rhythmic flashes. From Greek plays to Western opera, our most popular entertainment forms have made use of combinations of lights and sounds. Some composers, such as the visionary Scriabin, actually created music intended to be experienced in combination with rhythmic light displays.”
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.
Deeper Meditation • Near The Stage Of Sleep • Vivid, Dreamlike Imagery • Creative Visualization • Feel More Open & Connected • Advanced Problem Solving • Super Creativity • Insight • Intuition • Inspiration • Deeper Subconscious To Super-Conscious Mind • Trance-like • GABA • Immune System • Serotonin • Endorphins • Acetylcholine • Lower Cortisol • Deeply Relaxed • Sleep Better • Emotional Intelligence

Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 

Pure tones played together interfere with each other when they are close in pitch but not identical. When each tone is sent to a different ear, there will not be any physical interaction between the waves, yet your brain still creates an interference inside your head: the so-called binaural beat. In order to create a binaural beat, each ear must receive its dedicated signal. Therefore, binaural beats only work through headphones.