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.
Meanwhile, the therapeutic benefits of listening to sound and music is a well-established principle upon which the practice of receptive music therapy is founded. The term 'receptive music therapy' denotes a process by which patients or participants listen to music with specific intent to therapeutically benefit; and is a term used by therapists to distinguish it from 'active music therapy' by which patients or participants engage in producing vocal or instrumental music.[37] Receptive music therapy is an effective adjunctive intervention suitable for treating a range of physical and mental conditions.[38]

Delta brain state is related to the unconscious or super-conscious mind. Delta waves are the slowest of all five brainwave frequencies. These brain waves are generated in deep sleep and in very deep meditation. In the sleep cycle, the deepest of sleep states is called “Slow Wave Sleep” (SWS). In this phase, the brain begins producing very slow, large Delta waves. The deeper the sleep, the higher the amount of delta waves. This stage plays a vital role in health and well-being, especially because healing and regeneration processes are stimulated in this state. In the Delta state, you do not dream, you are completely unconscious.
There are five main categories of brainwave frequencies: Gamma (40Hz+), Beta (13 – 40Hz), Alpha (7 – 13Hz), Theta (4 – 7Hz), and Delta (<4Hz). Each category is associated with a different state of mind; so, for example, when you’re in a peak state of performance, your brain produces Alpha Waves, and when you’re in a deep sleep, your brain produces Delta Waves.
In addition to understanding how exercise can help manage stress and the types of exercise to recommend for stress management, it is important to understand common barriers that might affect exercise participation in high-stress clients. Lack of time is the most commonly reported exercise barrier for individuals in general. A lack of motivation, fatigue, poor sleep habits, and poor dietary habits are factors associated with stress that can negatively impact exercise compliance and adherence (4). Common exercise barriers and stress-related health problems should be taken into consideration when developing an exercise prescription for high-stress individuals.

Another very useful application for the Theta & Delta frequencies is to keep your eyes open while listening to the entrainment recordings. Simply pick a spot on the wall and look beyond it as if you were looking at the view beyond the wall. Keeping your eyes open while in Theta and Delta brainwave states stimulates connections between the visual information processing centers of your brain and the "dream vision" centers that normally only function with the eyes closed.
Everyone knows stress can cause you to lose sleep. Unfortunately, lack of sleep is also a key cause of stress. This vicious cycle causes the brain and body to get out of whack and only gets worse with time. Make sure to get the doctor-recommended seven to eight hours of sleep. Turn the TV off earlier, dim the lights, and give yourself time to relax before going to bed. It may be the most effective stress buster on our list.
So if you are interested in using brainwave entrainment music in your own recording, do so with the knowledge that it can only help to improve the quality of your work. But please don’t feel as though your recordings will be insufficient without it (some people do worry about this - unnecessarily). My advice is that if you ever find yourself in a situation where the music you love the most is not available with brainwave entrainment frequencies, don’t ignore your intuition and discard that music. When you find that piece of music that brings your recording to life, go with it whether it has brainwave entrainment frequencies or not. The quality and feel of the music itself are the most important factors.
Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
When you play a tone with a slightly different frequency into your left and right ear — say, 200 hertz (Hz) in one and 210 Hz in the other — they travel separately to your inferior colliculus, the part of your brain that gathers auditory input. There, the tones “squelch” together into a so-called “beat” at a perceived new frequency. (In this case, it would be 10 Hz.)
Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.
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]