Quick example: Brainwave readings (with an EEG machine) have shown that brainwaves of 2Hz occur when an individual is asleep. Scientists can create special audio recordings, which contain an encoded 2Hz frequency. While listening to such audio, the brain naturally follows (entrains) toward that 2Hz frequency, lowering its brainwave patterns. That's "brainwave entrainment." The net result is that when listening to such an audio recording, you (the listener) will naturally fall asleep.
One RCT (n=108) showed significant reduction in anxiety from a single session of alpha/delta therapy for day surgery patients. A crossover RCT of a single session of theta stimulation in four healthy adults reported significant improvement from the intervention in one of five measures. Five pre/post studies reported significant benefit from the intervention for 16 of 27 outcomes.

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So, what is binaural beats or binaural tones?  They are auditory (hearing) processing artifacts, or apparent sounds, caused by specific physical stimuli.  This effect was discovered in 1839 by Heinrich Wilhelm Dove and earned greater public awareness in the late 20th century based on claims coming from the alternative medicine community that binaural beats could help induce relaxation, meditation, creativity and other desirable mental states. The effect on the brainwaves depends on the difference in frequencies of each tone: for example, if 300 Hz was played in one ear and 310 in the other, then the binaural beat would have a frequency of 10 Hz.
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]
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