Thanks for your appreciation of what I’m doing. I’ve been asked for help with autism a number of times over the years, so it’s something that I’ve often looked into and tried to find new information about. Unfortunately, I’ve yet to find any specific research relating to it and using the type of brainwave entrainment tones I use. There are a number of opinions and claims out here, but I’ve often found them to be conflicting. While some are recommending higher frequency gamma waves, others are recommending lower frequency alpha and theta waves while meditating.
Binaural beats were discovered in 1839 by a German experimenter, H. W. Dove. The human ability to "hear" binaural beats appears to be the result of evolutionary adaptation. Many evolved species can detect binaural beats because of their brain structure. The frequencies at which binaural beats can be detected change depending upon the size of the species' cranium. In the human, binaural beats can be detected when carrier waves are below approximately 1000 Hz (Oster, 1973). Below 1000 Hz the wave length of the signal is longer than the diameter of the human skull. Thus, signals below 1000 Hz curve around the skull by diffraction. The same effect can be observed with radio wave propagation. Lower-frequency (longer wave length) radio waves (such as AM radio) travel around the earth over and in between mountains and structures. Higher-frequency (shorter wave length) radio waves (such as FM radio, TV, and microwaves) travel in a straight line and can't curve around the earth. Mountains and structures block these high-frequency signals. Because frequencies below 1000 Hz curve around the skull, incoming signals below 1000 Hz are heard by both ears. But due to the distance between the ears, the brain "hears" the inputs from the ears as out of phase with each other. As the sound wave passes around the skull, each ear gets a different portion of the wave. It is this waveform phase difference that allows for accurate location of sounds below 1000 Hz(9). Audio direction finding at higher frequencies is less accurate than it is for frequencies below 1000 Hz. At 8000 Hz the pinna (external ear) becomes effective as an aid to localization. In summary it's the ability of the brain to detect a waveform phase difference is what enables it to perceive binaural beats.
There is no single relaxation technique that is best for everyone. The right relaxation technique is the one that resonates with you, fits your lifestyle, and is able to focus your mind and interrupt your everyday thoughts to elicit the relaxation response. You may even find that alternating or combining different techniques provides the best results. How you react to stress may also influence the relaxation technique that works best for you:

Brainwave Entrainment is the process of synchronizing the brain to specific frequencies and patterns embedded in audio tracks. These frequencies correlate to specific emotions, feelings, and even energy levels. Using nothing more than sound, Brainwave Entrainment can enhance creativity, change moods, and even alter behavior like sleep and energy levels.

Your brainwave activity during sleep is largely distinct from your brain activity when you’re awake. (REM sleep is one exception to this—during REM, your brain is active in ways very much like when you’re awake.) During non-REM sleep, the slower, lower frequency theta and delta waves dominate, compared to the alpha and beta waves that are prominent when you’re alert and active.

Exercises improves insulin sensitivity, can help someone become more aware of their hunger levels, improves confidence/self-esteem, and leads to better mental processing and a lower risk for depression. (2) Can’t sleep? Well, exercise can help with that too, which is very important considering quality sleep is needed to regulate hormones and help the body recover.
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.  

That’s why it’s so important to find the proper stress relievers to maintain a strong quality of life. The eight stress relievers above — exercise and yoga, meditation/healing prayer, acupuncture, a nutrient-dense diet, cognitive behavioral therapy, spending more time in nature and being social, keeping a journal and using adaptogen herbs and essential oils — can help you maintain a good mood, remain calm and better handle your day-to-day stress.
Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.

Stress: We all deal with it, yet we know how much better off we’d be — both physically and mentally — if we could only get it under control and find stress relievers that really work. While stress can be a positive, motivating factor at times (such as when you’re under pressure to perform well at work or to ace an important exam), more and more research shows that chronic stress impacts the body in ways similar to a poor diet, lack of sleep or sedentary lifestyle.
Recent research at the University of Lisbon finally uncovered the reason for the 350 year-old mystery, finding that the resonance of sound is the mechanism for entrainment of swinging pendulums and ticking clocks, and it seems likely that the energy transferred by sound is also responsible for other observations of entrainment, including brainwave entrainment.
Effects on cortisol: The hormone cortisol is commonly associated with stress, and when levels are higher than usual, it can have a negative impact on the body. High levels of cortisol can lead to a range of conditions, including Cushing syndrome, menstrual cycle and female libido changes, anxiety, and depression. Dr. Giampapa noted a reduction of cortisol of up to 70-80 percent in several study participants.
There’s an aesthetic element to the music and there are a lot of drone-based sounds and time-stretched sounds, deep, rich bass sounds—there’s a spectrum of sounds within there—and what’s more, there’s a load of 3D processing that goes on to ensure that the mind doesn’t become habituated to them. There’s also a constant, subtle sense, a slow and gradual sense, of the sounds shifting around. And, there are layers of binaural beats.
Brainwave entrainment is a field of study and endeavor founded in the same physiological and psychological processes that make music, drumming, and chanting so powerful as methods for transforming the mind and spirit and aiding in healing of the body. These processes involve how the electrical energy in our brains synchronizes with sounds and visual stimuli, producing a particular brainwave frequency and its associated mental states. 
LEARNING OBJECTIVE • Exercise can be an effective component of a stress management program, and all types of exercise can be beneficial for stress management. Exercise programs consistent with the current recommendations to improve health can be prescribed to manage stress. Fitness professionals should recognize that it might be necessary to refer a client to a psychologist or other health care provider to help develop strategies for managing stressors that produce chronic and acute episodic stress.
In fact just having a particular range of brainwaves running through our grey matter is also not “meditation”. Brainwaves are not the cause of the meditative state. They are only an indicator that we might be in a meditative state. And then again we might be in some other state as well. Those exact same brainwave frequencies are present during many different activities and states of consciousness, not just during meditation.
In order to understand brainwave entrainment you first have to understand something about brain waves and electroencephalograms (EEG). Neurons are cells that communicate with each other through electrical conduction. When a neuron fires it creates a small electrical and magnetic field. These fields are far too small to measure by placing electrodes on the scalp, or even on the surface of the brain. The only reason we can detect the electrical fields of the brain is because many neurons are firing together – in synchrony. All brain waves that are measured by an EEG, therefore, represent a large group of neurons firing together.
It cannot be any wonder then that we are almost desperate to find some sign, some indication that meditation and brainwave entrainment is having tangible, definable effects. We seize on these odd little experiences like ‘flushing of the face’ or ‘seeing spirals of color’ when our eyes are closed, hoping these are signs suggesting the elusive relief we’ve been after is finally within our grasp. We ask others to validate our experiences so that we can reassure ourselves we’re on the right track at last.

Everyone experiences stress, and not all stress is bad. However, individuals who experience acute episodic and chronic stress are at increased risk for developing stress-related health problems. This article outlines the relationship between stress and health and discusses the role of exercise in managing stress. Exercise recommendations and stress management tips are provided.

Most of the tips we’ve suggested provide immediate relief, but there are also many lifestyle changes that can be more effective in the long run. The concept of “mindfulness” is a large part of meditative and somatic approaches to mental health, and has become popular in modern psychotherapy. From yoga and tai chi to meditation and Pilates, these systems of mindfulness incorporate physical and mental exercises that prevent stress from becoming a problem. Try joining a class.
Research: the authors stated that qualitative electroencephalogram signatures needed to be developed for different disorders and tested using standard validated methods of psychological assessment. Larger RCTs were needed with clear inclusion criteria for participants. The RCTs should measure qualitative EEG, hormone levels and the time of day of the intervention. Interventions protocols should be clearly defined and the relationship between session frequency/ duration and outcomes should be explored. More studies of auditory stimulation were needed, as well as studies comparing different types of stimulation, monaural, binaural and isochronic beats and use of white noise versus music.
Rudy's primary work is on Alzheimer's. In this disease, beta amyloid proteins form plaques in the brain and kill nerve cells eventually leading to dementia. Research from Washington University School of Medicine in St. Louis shows that when people's brains are in a Delta brain wave state, beta amyloid production in the brain ceases and the toxic material is cleared away. One thought is to explore the possibility of using brain entrainment technology to help treat Alzheimer's, but at this point all it is being used for is to help people meditate, relax and dream instantly and effortlessly.

Synchronized brain waves have long been associated with meditative and hypnogogic states, and audio with embedded binaural beats has the ability to induce and improve such states of consciousness. The reason for this is physiological. Each ear is "hardwired" (so to speak) to both hemispheres of the brain (Rosenzweig, 1961). Each hemisphere has its own olivary nucleus (sound-processing center) which receives signals from each ear. In keeping with this physiological structure, when a binaural beat is perceived there are actually two standing waves of equal amplitude and frequency present, one in each hemisphere. So, there are two separate standing waves entraining portions of each hemisphere to the same frequency. The binaural beats appear to contribute to the hemispheric synchronization evidenced in meditative and hypnogogic states of consciousness. Brain function is also enhanced through the increase of cross-collosal communication between the left and right hemispheres of the brain.

The Transparent Corp forum – This forum is an invaluable resource for any brainwave entrainment user or enthusiast.  Most of the feedback is obviously focused on the Transparent Corp software, but with over 20,000+ posts now you can find answers to the whole array of brainwave entrainment questions on there.  (UPDATE: Sadly, the Transparent Corp forum has now been taken offline)

Some people deny there is any such thing as “spiritual”. Atheists, secular humanists, etc., do not as a rule accept the concept of the existence of things “spiritual.” For them the benefits of meditation are largely physical and/or emotional in nature. It is not my intention to dispute or attempt to change their views here. What I can say is that they are free to skip over any mention of things spiritual and focus on the physical/emotional aspects. Meditation is a broad enough discipline to encompass all these areas of our existence.

Theta brainwaves in the frequency range of 6 to 9 hertz are known as thalpha waves because of their proximity to alpha waves. They are seen during states of high suggestibility, during hypnosis, and during paranormal experience and are also connected to an increase in human growth hormone (HGH) levels and higher blood flow to the brain. Theta brainwaves sit between the realms of the subconscious and conscious mind, making them an especially useful brainwave state for developing creative thinking, working through emotional problems, and integrating subconscious and conscious experience. 
When stress attacks, it can feel like your whole world is crashing down. Remind yourself what’s good in your life with a quick gratitude round-up. “Studies show gratitude techniques like counting your blessings can be a significant stress reducer,” Dr. Serani says. “Gratitude research reports that those who utilize daily gratitude reflections have higher levels of positive emotions, life satisfaction, vitality, optimism, and lower levels of depression and stress.” Reminding yourself of the good things in life can put stress in perspective. “Studies show that cultivating an optimistic mindset can help you maintain a positive mood,” Whitaker says. “When you are positive and grateful, you are able to handle difficult situations better.” Just look out for these stress relievers that actually backfire.

Gamma brainwaves occur during creative thinking and processing of memory and language and in many learning activities. These brainwaves are not present at all when a person is under anesthesia, but return as soon as the person becomes conscious again. Multiple scientific studies have shown gamma brainwave entrainment to be helpful for reducing distractibility, improving short-term memory, improving motor coordination, and relieving migraine headaches.

Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.