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Benefits:

A. Reduced Anxiety:
In 2001, a study was conducted with the objective of determining "whether mildly anxious people would report decreased anxiety after listening daily for 1 month to tapes embedded with tones that create binaural beats."

The experiment was performed with a volunteer sample of 15 mildly anxious patients. Participants were asked to listen to the tapes at least 5 times a week for 4 weeks, and to record tape usage, anxiety ratings, and other comments in a journal during the study.

The most frequent comments included in patient journals were about enhanced relaxation and falling asleep. Many indicated that as the study progressed, the relaxing effects of the simulation began earlier during a session. They reported that being relaxed helped them to experience sleep onset faster, to sleep better, and to awake more rested. Many comments indicated that participants had a hard time staying awake when listening to the tapes, and they sometimes reported that they fell asleep with the tape still running.

Participants were asked to rate their anxiety on a scale of 1 to 100, with 1 indicating no anxiety, and 100 marking very high anxiety. Before listening to the tapes, the average score reported was 43.1. After listening, the average dropped significantly, to 24.3.

The study's authors concluded: "Listening to binaural beat tapes in the delta/theta electroencephalogram range may be beneficial in reducing mild anxiety."

Source: Le Scouarnec RP, Poirier RM, Owens JE, Gauthier J, Taylor AG, Foresman PA. Use of binaural beat tapes for treatment of anxiety: a pilot study of tape preference and outcomes. Altern Ther Health Med. 2001;7(1):58-63

B. Hypnotic Induction:
William S. Kroger, M.D., in his influential 1959 study regarding hypnotic induction, began the article with the following observation:
"In the year 1784, Benjamin Franklin, a pioneer in electricity, denounced as a fraud, Mesmer, a pioneer in hypnosis. Today, 175 years later, the work of one is aiding the work of the other as electronic devices induce the hypnotic state."

Kroger and Schneider tested the Brainwave Synchronizer on 2,500 patients before writing their report. When their data from all the tests was combined, they found that the photic stimulation provided by the device was able to induce a hypnotic state in just over 5 minutes, for nearly 80% of subjects- and of those subjects, the percentage of deep hypnosis inductions was twice that of those who remained in light hypnosis.

"Expectation level" was found to play a role in the success of hypnotic induction produced by the photic stimulation. Subjects who entered the experiment "cold," with no previous explanation regarding the device and hypnosis, were less likely to be inducted. But "when the instrument was used as the final part of a program containing several demonstrations of hypnosis in the conventional manner and a detailed explanation of what the instrument will do" the hypnosis induction

However, prior experience with being hypnotized was not found to be a significant factor in this study. The authors kept separate figures for groups with and without previous hypnotic experience, and found only a negligible difference in the results between the two.

Since that 1959 study, ongoing research has further solidified the connection between brainwave stimulation, theta brain wave activity, and ease of attaining a state of hypnosis.

With two subjects who were minimally responsive to hypnosis, Wickramasekera (1977) found that after 10 sessions of deep theta stimulation, including suggestions encouraging hypnotic responsiveness, the subjects increased an average of 6.5 points on a 12-point hypnotizability scale.

And Sabourin (1990) found that, "in eyes open and closed conditions in waking and hypnosis, highly hypnotizable subjects generated substantially more mean theta power than did low hypnotizable subjects at all occipital, central and frontal locations in almost all conditions of waking and hypnosis."

Source:
Kroger, W. S., & Schneider, S. A. (1959). An electronic aid for hypnotic induction: A preliminary report. International Journal of Clinical and Experimental Hypnosis, 7(2), 93-98.
Wickramasekera I, I. E. (1977). On attempts to modify hypnotic susceptibility: Some psychophysiological procedures and promising directions. Annals of the New York Academy of Sciences, 296, 143-153
Sabourin, M. E., Cutcomb, S. D., Crawford, H. J., & Pribram, K. (1990). EEG correlates of hypnotic susceptibility and hypnotic trance: spectral analysis and coherence. International Journal of Psychophysiology, 10(2), 125-142.

C. Zen Meditation:
Observations of the connection between increased theta activity and meditation practice go all the way back to 1966 (Kasamatsu). Cahn (2006) lists 29 individual studies showing a correlation between theta activity and active practice of various meditative traditions- primarily Zen and Transcendental Meditation.

One of the more recent studies (Takahashi, 2005) monitored EEG activity in 20 adult Zen practitioners.

This study specifically utilized "So-soku," a Zen meditation practice for concentrating the mind by slowly counting one's breaths. In Su-soku, the subject starts counting 'one' when they exhale, and inhale naturally without counting. The counting continues until the subject reaches 'one hundred' and the subject then starts again from 'one.' If other thoughts occur, the subject lets them pass and restricts their attention to counting.

As a control condition, participants were asked to simply try to keep their breathing regular for 15 minutes, and EEG data was monitored for that time. Afterwards, participants left the room for a 30 minute rest period, before returning to perform the So-soku meditation for 15 minutes.

When the EEG data collected during the respective 15 minute periods was analyzed, significantly higher theta power was detected during the meditation practice vs. the control condition.

Personality trait factors were also analyzed during this experiment. And it was found that the percent change in fast theta power in the frontal area, reflecting enhanced mindfulness, was positively correlated with the harm avoidance score. As the authors noted, this has been suggested to be associated with increased serotonin activity.