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.

There isn’t really a one-size-fits-all track or frequency range which is right for all kids while doing homework. So that does make it difficult to recommend one thing in particular, and why I have a number of tracks for studying and focus. If they have already learnt and understood the information, but are just trying to commit it to memory for a test, then I would recommend an alpha track, like the Memorization Study Aid product I have with the 10.4Hz frequency you referred to. If they are still trying to fully understand what is being taught in a workbook, then I would recommend a track that is mainly beta frequencies, like my Study Focus tracks. In the middle, I have a number of tracks which use a combination of beta and alpha wave frequencies, like Study Booster, Study Enhancer and Cognition Enhancer. The last 3 use similar frequencies but deliver the tones and brainwave entrainment effects in different ways. As we are all wired a little differently it does sometimes take a bit of trial and error, to see what method or frequency range works best for the individual. These types of tracks are made for a general audience. In an ideal world, you would hook up to an EEG and see in real time exactly what a person responds to best, depending on the goal and current state of mind.
A study published in Electroencephalography and Clinical Neurophysiology by Paul Williams and Michael West in 1975 examined the brainwave states of people experienced in meditation while using photic stimulation, and another study by Leonard, Telch, and Harrington in 1999 examined the successful use of brainwave entrainment techniques for attaining meditative states in subjects.

“…humans have always been intrigued by the possibilities for influencing mental functioning that emerge from combining rhythmic sound and rhythmic light stimulation. Ancient rituals for entering trance states often involved both rhythmic sounds in the form of drum beats, clapping, or chanting and flickering lights produced by candles, torches, bonfires, or long lines of human bodies passing before the fire and chopping the light into mesmerizing rhythmic flashes. From Greek plays to Western opera, our most popular entertainment forms have made use of combinations of lights and sounds. Some composers, such as the visionary Scriabin, actually created music intended to be experienced in combination with rhythmic light displays.”
I have seen 1.5Hz being linked to HGH, but also 4 or 5 other frequencies as well, so it’s difficult to know what may work if any. I haven’t seen any research relating to HGH and brainwave entrainment. It’s widely believed that 40Hz is the limit for achieving a brainwave entrainment effect, which is also where many believe the gamma frequency range begins. Once you get over 40Hz into gamma your brainwave activity isn’t likely to stay in sync with it. So from a brainwave entrainment perspective, I recommend high beta frequencies for increasing energy during workouts.
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.
One of the first pieces of research into using binaural beats as a sleeping aid was In a paper called “Tests of the Sleep Induction Technique” published in 1975 by Dr Arthur Hastings. He noted the effects of subjects who listened to a tape containing binaural beats starting from beta slowly descending to delta. Using an EEG machine he was able to monitor the subject’s brainwaves as they listened to the tape, becoming increasingly relaxed before falling asleep. He concluded; “patterns in the various stages suggested that the tape was influencing the subject’s state”.
Binaural beats are not a physical noise or sound per se. Rather binaural beats are a sort of phantom tone which is manufactured by the brain when two different tones are played in each ear. For the binaural beat to be perceived you need stereo headphones and the frequency of the two different tones coming into each ear must be below 1000hz, and no more than 30hz apart. If they are more than 30hz apart you will simply hear a tone in each ear, one louder than the other. But if the difference between the beats is below 30hz you hear the binaural beats.
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