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: The corresponding MP3 versions for those tracks can be found on my site here: I hope that helps.
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.
Gamma waves are the fastest of the brainwave frequencies (high frequency band of brainwave activity) which signifies the highest state of focus possible. They are associated with peak concentration and the brain’s optimal frequency for cognitive functioning – the 40 Hz frequency corresponds to a Schumann resonance band and many scientists, including Nobel Laureate Sir Francis Crick believe that it may be the key to the act of cognition. The Gamma state relates to simultaneous processing of information from different brain areas; information passes very rapidly.
After you fully understand the above principles, the next source of poor results to consider arises from faulty expectations and misunderstandings about what meditation and brainwave entrainment are, and what the experience of either one of them is like. Meditation and Brainwave entrainment aren’t synonyms but the misunderstandings about them do have some overlapping areas. Some misunderstandings are common to both while some are unique to one or the other.

Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 
Joseph Kao, creator of Profound Releasing, Profound Renewal, and Sound Asleep, is a hypnotherapist and a solution-focused therapist with a private practice in Cambridge, UK. Joe was the co-developer of an acclaimed course on conversational hypnosis, and he regularly teaches hypnotherapy and psychotherapy to other therapists. He has also been the head scriptwriter for over 800 professional hypnotherapy recordings. Joe was drawn to the world of philosophy, meditation, and brainwave entrainment technology from an early age, and he’s had a daily meditation practice since 1998.
(Shannahoff-Khalsa, 1991; Webb & Dube, 1981). These naturally occurring shifts may underlie the anecdotal reports of fluctuations in the effectiveness of binaural beats. External factors are also thought to play roles in mediating the effects of binaural beats (Owens & Atwater, 1995). The perception of a binaural beat is, for example, said to be heightened by the addition of white noise to the carrier signal (Oster, 1973), so white noise is often used as background. "Music, relaxation exercises, guided imagery, and verbal suggestion have all been used to enhance the state-changing effects of the binaural beat" (Owens & Atwater, 1995). Other practices such as humming, toning, breathing exercises, autogenic training, and/or biofeedback can also be used to interrupt the homeostasis of resistant subjects (Tart, 1975).
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.
Your brain cells reset their sodium & potassium ratios when the brain is in Theta state. The sodium & potassium levels are involved in osmosis which is the chemical process that transports chemicals into and out of your brain cells. After an extended period in the Beta state the ratio between potassium and sodium is out of balance. This the main cause of what is known as "mental fatigue". A brief period in Theta (about 5 - 15min) can restore the ratio to normal resulting in mental refreshment.  

Changes in neural oscillations, demonstrable through electroencephalogram (EEG) measurements, are precipitated by listening to music,[20][21][22][23][24][25] which can modulate autonomic arousal ergotropically and trophotropically, increasing and decreasing arousal respectively.[26] Musical auditory stimulation has also been demonstrated to improve immune function, facilitate relaxation, improve mood, and contribute to the alleviation of stress.[27][28][29][30][31][32][27][33] These findings have contributed to the development of neurologic music therapy, which uses music and song as an active and receptive intervention, to contribute to the treatment and management of disorders characterized by impairment to parts of the brain and central nervous system, including stroke, traumatic brain injury, Parkinson's disease, Huntington's disease, cerebral palsy, Alzheimer's disease, and autism.[34][35][36]