, that is, the average of the two frequencies. It can be noted that every second burst in the modulation pattern is inverted. Each peak is replaced by a trough and vice versa. However, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. Therefore, subjectively, the frequency of the envelope seems to have twice the frequency of the modulating cosine, which means the audible beat frequency is:[5]

Of course, meditation is actually quite a simple procedure, and one that can be practiced anywhere and at any time. There are no special requirements other than the need to have peace and quiet in a distraction-free environment for a few minutes. The trick is being able to switch off from whatever is going on around you and let your meditative state begin.


Meditation Begins • Mind Chatter Slows Down • Great For Learning & Studying • Creative Ideas Flow • Reverse Brain’s Aging • Habits, Fears, Phobias Melt Away • Calm & Peaceful • First Layer Of Subconscious Mind • Gateway To Deeper Mental States • Advanced Focus • Relaxation Begins • Serotonin • Endorphins • Good For Anxiety, Depression, Stress, Panic • Mind Power • Happiness • Confidence


In 1973, biophysicist Dr. Gerald Oster published a famous article in Scientific American titled “Auditory Beats in the Brain”, which found that when two pure tones of varying frequencies were combined, a third rhythmic beat was created which he called binaural or monaural beats. According to Oster, monaural beats occur when two tones are combined and sent through a loudspeaker, while binaural beats occur when stereo headphones are used to deliver each tone separately to each ear. Oster concluded that monaural beats were a more effective form of brainwave entrainment.

In addition to potentially boosting sleep-promoting hormones, binaural beats may also reduce our perceptions of pain. A 2017 study found binaural beats used in combination with visual stimulation led to reductions in patients’ perception of acute pain. Other recent research showed binaural beats helped improve pain perception in patients with chronic pain.


However, those with ASD are sometimes also diagnosed with ADHD. Although they are different conditions, some of the symptoms can be intertwined, which it appears may be the case with your grandson. So I would start by trying out my tracks for ADHD. You can try those out for free on my YouTube channel and I’ve put them together in a playlist here: https://www.youtube.com/watch?v=RKao2oZZPnw&list=PLveg0IEcZWN5iVmMduR9UjLzX_YgCetds. The corresponding MP3 versions for those tracks can be found on my site here: https://www.mindamend.com/intelligence-and-brain-power/. I hope that helps.
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.
Participants in the included studies were children and adults, either healthy or with conditions such as learning disabilities, attention deficit hyperactivity disorder, migraine, stress, anxiety and myofascial pain. Interventions included single, alternating, ascending or descending frequencies of photic or auditory stimulation or audiovisual entrainment selected either by the participant or by the investigator. Nearly half the studies used single sessions and the rest used multiple sessions ranging from nine to 100. Length of session varied from 0.5 seconds to 60 minutes. Frequency of session varied from twice daily to weekly. Outcomes reported in the review included cognition (including verbal skills, performance skills, attention, memory and overall intelligence/achievement), short- and long-term stress, pain, headache/migraine, mood, behavioural problems and premenstrual syndrome (PMS).
As the ancient cultures believed that sound waves of different frequency and beats could induce a state of meditation. Ancient Hindus and Yogis believed that specific kind of sound waves can induce relaxing effects. I found the best binaurial beat app BINAURAL BEATS - MEDITATION & RELAXATION - Apps on Google Play as it is designed to provide you with the best meditation, deep sleep, stress relief, healing and sleep sounds.
Binaural beats are created from two different continuous tones, which when sent separately to each ear create a single beat inside your head. Isochronic tones are basically a single tone which is switched on and off at regular intervals. Imagine a single continuous tone playing on a stereo system and you’ve got your hand on the volume switch. Then once per second, you turn the volume off for half a second and keep doing that every second. For half a second the volume is off, for the other half a beat waveform is formed. The beat is cycling once per second per second, i.e. at a rate of 1Hz.

Similar results have been achieved with the use of music alone, the most famous example being the so-called Mozart effect. In his book "Pourqui Mozart?" Dr. Alfred A. Tomatis claims that the composer’s music promoted healing and brain development[1]. The idea has been further popularized by Don Campbell in his book "The Mozart Effect", which claims that listening to Mozart can temporarily boost a person’s scores on portions of an IQ test [2].
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself. 
People who meditate grow bigger brains than those who don't. Researchers at Harvard, Yale, and the Massachusetts Institute of Technology have found the first evidence that meditation can alter the physical structure of our brains. Brain scans they conducted reveal that experienced meditators boasted increased thickness in parts of the brain that deal with attention and processing sensory input.
The objectives and inclusion criteria of the review were clear. Relevant sources were searched for studies, although the restriction to published studies in English meant that the review was prone to publication and language biases. The authors did not state whether steps were taken to minimise the risk of bias and error in the processes of study selection and data extraction (for example, by having more than one reviewer independently make decisions). The authors mentioned which studies were blinded, but it did not appear that study validity was systematically assessed, which made it difficult to judge the reliability of the review findings. The decision to combine studies by narrative synthesis appeared appropriate given the strong clinical heterogeneity between the studies, but the authors failed to quantify the size or statistical significance of the findings reported. The evidence presented appeared to justify the authors’ conclusions that further research was justified, but in view of the dearth of good-quality evidence and problems with methodology and reporting in the review, the conclusions regarding efficacy did not appear reliable.
Until recent years, entering extraordinary states of heightened receptivity and peak performance has been attained predominantly by only a disciplined few, practicing ancient techniques such as meditation, chanting, yoga, and newly revamped versions of the mystical traditions - for example, progressive relaxation, auto-suggestion, hypnosis, and biofeedback. These techniques work. But they take long periods of practice, discipline, and sometimes a leap of faith. It is all too easy to become impatient and give up long before producing results.
Newberg, who was catapulted to center stage of the neuroscience-religion debate by his book and some recent experiments he conducted at the University of Pennsylvania with co-researcher Eugene D'Aquili, says he has a sense of his own spirituality, though he declined to say whether he believed in God because any answer would prompt people to question his agenda. "I'm really not trying to use science to prove that God exists or disprove God exists," he said. Newberg's experiment consisted of taking brain scans of Tibetan Buddhist meditators as they sat immersed in contemplation. After giving them time to sink into a deep meditative trance, he injected them with a radioactive dye. Patterns of the dye's residues in the brain were later converted into images.
So, in summary, binaural beats certainly do not work the way the sellers claim, but there's no reason to think they're any less effective than any other music track you might listen to that effects you in a way you like. If they make you sleepy (like they all do for me), use them to go to sleep. If they relax you or get you amped, use them for that. But don't expect them to be any more effective than regular music. If someone you know claims that they are, put them to the test, and bust the myth.
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