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.
When we first use brainwave entrainment, we may not have anything specific in mind that will happen, but we hold a general expectation that “something” should happen. As we begin the process of entrainment we are on high alert looking for any little indication that something is happening. Pretty soon we identify some feeling or twitch or unusual perception. The moment we focus on whatever it is, the act of focusing on it magnifies the thing. Since we were already viewing the situation with an expectation that it was the entrainment that was going to produce some sort of result, we automatically associate whatever our phenomenon is with entrainment.
Robert Monroe, a radio producer and executive published a popular book called Journeys Out of the Body about his out-of-body experiences when using brainwave entrainment. He later founded an original brainwave entrainment audio company, Hemi Sync. In 1981, the book Mega Brain by Michael Hutchison brought brainwave entrainment information, techniques, and terminology into the popular press.
... Several studies have looked at the possible effects of binaural beats within the alpha range on cognitive abilities. A significant improvement in cognitive processing, as measured by the Stroop Effect exercise, was found by a BB stimulation of 10.2 Hz frequency (Cruceanu & Rotarescu, 2013).Carter and Russell (1993)exposed 8 to 12 year old boys with learning disabilities to 8-week long 10 and 18 Hz BB stimulation sessions, and they found an improvement in Raven's progressive matrices and in a subtest of auditory sequential memory (Carter & Russell, 1993).McMurray (2006)assessed the effect of 7 and 11 Hz BB on alpha brainwave activity, working memory, and attention in healthy elderly people, who are known for experiencing gradual decrease in physiological alpha activity. The 2 minutes exposure to BB resulted in an altered electrical activity in the brain. ...

A large dose of caffeine causes a short-term spike in blood pressure. It may also cause your hypothalamic-pituitary-adrenal axis to go into overdrive. Instead of coffee or energy drinks, try green tea. It has less than half the caffeine of coffee and contains healthy antioxidants, as well as theanine, an amino acid that has a calming effect on the nervous system.
The huge problem will all such studies is that there is a clear placebo effect on any kind of mental performance whenever the subject is observed. Do any intervention, then measure performance, and the intervention and measurement are likely to cause an increase in effort and attention which will increase performance. This generic “placebo” effect needs to be factored out of any such study by proper blinding and controls in order for the results to have any meaning at all.
The mantra technique as taught by Michael at Project Meditation is an excellent example of an outward technique. Since the vast majority of people have somewhat active minds, this mantra technique is a good bet for most of us. Even mantra techniques have some differences. Some require rigid concentration while others are more relaxed, such as Michael’s technique. There are some that use chanting which is helpful for a person whose mind is hyperactive.
The activity of neurons generate electric currents; and the synchronous action of neural ensembles in the cerebral cortex, comprising large numbers of neurons, produce macroscopic oscillations. These phenomena can be monitored and graphically documented by an electroencephalogram (EEG). The electroencephalographic representations of those oscillations are typically denoted by the term 'brainwaves' in common parlance.[4][5]