While the physiological and psychological processes being uncovered by brain science in the study of brainwaves is sometimes complex and still being investigated, certain basic principles are well-established, easily understood, and helpful for achieving the most effectively use of brainwave entrainment when seeking relaxation, improved sleep, lowering of anxiety, or other goals. This important background information and scientific knowledge presented here includes: 
This is probably the most popular choice of frequency. The theta state is a state of tremendous stress relief. The benefits associated with theta level relaxation include improved concentration, reduced hyperactivity and improved memory. While in a state of theta relaxation, one’s blood pressure, breathing and heart rate all slow to a much more restful and healthy level that promotes natural healing. During theta relaxation one may also experience vivid flashes of mental imagery as the mind opens to memories or subconscious information that is not available to the conscious mind during the normal waking state. The theta state is a very deep state of relaxation that is excellent for deep hypnosis and mental programming.
The Delta waves range from 1-3 Hz; these frequencies can assist in enhancing deep sleep. They also play a big role in boosting the immune system to facilitate natural body healing. The Theta waves have a frequency that ranges from 4-7 Hz. In turn, this brain state can enhance deep relaxation and is known to assist individuals who have poor memory. They are the best frequencies to use if you want to focus or meditate.
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.
The specific benefits and claims from this technology are often disputed and considered scientifically questionable. One problem is that there are few experiments that have utilized brainwave entrainment for the purpose of treating a specific psychological ailment (e.g. insomnia). And the experiments that have been conducted are largely backed by corporations that sell the software; hence it could be speculated that there are conflicts of interest.
Most programs start at a work/life busy brain Beta frequency of twenty light flashes per second (20Hz) and slowly ramp them down to Alpha (relaxation and meditation) at 8-12 HZ, Theta (deep relaxation and dreaming) at 4-8 Hz) and Delta (dreamless deep relaxation) of .5-4Hz. We have taken measurements at Mass General with state of the art EEG equipment and have seen a slowing of the brain waves from Beta to Theta in two minutes and complete brain wave harmonization in the left, right, anterior, posterior and occipital regions of the brain.
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.
Neural oscillations are rhythmic or repetitive electrochemical activity in the brain and central nervous system. Such oscillations can be characterized by their frequency, amplitude and phase. Neural tissue can generate oscillatory activity driven by mechanisms within individual neurons, as well as by interactions between them. They may also adjust frequency to synchronize with the periodic vibration of external acoustic or visual stimuli.[3]