Resonant entrainment of oscillating systems is a well-understood principle within the physical sciences. If a tuning fork designed to produce a frequency of 440 Hz is struck (causing it to oscillate) and then brought into the vicinity of another 440 Hz tuning fork, the second tuning fork will begin to oscillate. The first tuning fork is said to have entrained the second or caused it to resonate. The physics of entrainment apply to bio-systems as well. Of interest here are the electromagnetic brain waves. The electrochemical activity of the brain results in the production of electromagnetic wave forms which can be objectively measured with sensitive equipment. Brain waves change frequencies based on neural activity within the brain. Because neural activity is electrochemical, brain function can be modified through the introduction of specific chemicals (drugs), by altering the brain's electromagnetic environment through induction, or through resonant entrainment techniques.

“When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference, and a third tone of 9 Hz is experienced,” says Niraj Naik, founder of Trpynaural, a resource for binaural tracks. “This will result in your brain being raised or lowered and tuned into the desired frequency. This is how binaural beats are produced.”

The studies included in the recent reviews of Tai Chi and yoga indicate that sessions between 60 and 90 minutes performed 2 to 3 days per week were effective in reducing stress and improving feelings of well-being (7,14,17). A study conducted in a worksite environment showed that 15 minutes of chair-based yoga postures was effective in reducing acute stress when assessed by self-report and with physiological measures (e.g., respiration rate and heart rate variability parameters). This finding indicates that shorter duration sessions can be effective in reducing acute stress with this type of exercise (15).
Now I’m in the market for two extra tracks to have some variety. I have narrowed it down to a couple of ones including muscle relaxation which is theta and delta. I have a hard time relaxing my body. The last time my muscles where relaxed was after intensely cleaning my stove. I don’t want to clean every time I want to relax, even though my house will be spotless ;).
The objectives and inclusion criteria of the review were clear. Relevant sources were searched for studies, although the restriction to published studies in English meant that the review was prone to publication and language biases. The authors did not state whether steps were taken to minimise the risk of bias and error in the processes of study selection and data extraction (for example, by having more than one reviewer independently make decisions). The authors mentioned which studies were blinded, but it did not appear that study validity was systematically assessed, which made it difficult to judge the reliability of the review findings. The decision to combine studies by narrative synthesis appeared appropriate given the strong clinical heterogeneity between the studies, but the authors failed to quantify the size or statistical significance of the findings reported. The evidence presented appeared to justify the authors’ conclusions that further research was justified, but in view of the dearth of good-quality evidence and problems with methodology and reporting in the review, the conclusions regarding efficacy did not appear reliable.
Controlled or pre/post studies of the effects of BWE using auditory or visual stimulation were eligible for inclusion, provided pulses of light or tone were delivered at frequencies hypothesised to have a beneficial effect or in line with a protocol addressing clinical outcomes. Studies were required to report clinical or psychological outcomes (measured using standard methods or as deemed appropriate by peer review) and to report statistical analysis. Studies of outcomes such as electroencephalogram (EEG) response or neurotransmitter levels were not eligible. Case studies were excluded.
With its focus on full, cleansing breaths, deep breathing is a simple yet powerful relaxation technique. It’s easy to learn, can be practiced almost anywhere, and provides a quick way to get your stress levels in check. Deep breathing is the cornerstone of many other relaxation practices, too, and can be combined with other relaxing elements such as aromatherapy and music. While apps and audio downloads can guide you through the process, all you really need is a few minutes and a place to stretch out.
Stressed out after work? Need to relax and be focused before a test, exam, or interview?. This CD is for you. Wish I could explain how this CD works on your brain's "entrainment" but they do enclose a benefits description inside the CD case. It's amazing to listen to and see/feel the results after hearing the entire CD with a quality set of headphones on. Note: also works well with earbuds. I couldn't tell if the last track had played or not on the Nexus just takes you away then brings you back ... into something more structured and coherent.
The reason this rule of thumb is so useful is because there is a huge market for simple answers. A genuine elegant solution (one that accomplishes more with less) is highly valuable in the marketplace. We are used to technology delivering new easy solutions to previously difficult tasks. While most improvements are incremental, there are occasional breakthroughs that transform our lives.

Consider the following analogy. Imagine a ballroom full of people dancing together. When the music changes to a faster tempo, the dancers move faster in response to this. When a slower piece of music is played, the dancers’ rhythm slows down as well. In a similar way, the frequency of your brain will change in response to the frequency of the binaural beat that it is exposed to. For example, a person who is in a state of very deep meditation may have a dominant brainwave frequency of 5 hertz, so by listening to a binaural beat with a frequency of 5 hertz you can entrain your own brainwaves to a similar state.

Uses of audio with embedded binaural beats that are mixed with music or various pink or background sound are diverse. They range from relaxation, meditation, stress reduction, pain management, improved sleep quality, decrease in sleep requirements, super learning, enhanced creativity and intuition, remote viewing, telepathy, and out-of-body experience and lucid dreaming. Audio embedded with binaural beats is often combined with various meditation techniques, as well as positive affirmations and visualization.
When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference and a third tone of 9 Hz is experienced. This will result in your brain being lowered or raised and tuned into the desired frequency. This is how binaural beats are produced. Headphones are essential for this to work.  
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.