Business executive and radio producer Robert Monroe started experimenting with brainwave entrainment and has a series of powerful out of body experiences using it. In 1971 he published his cult classic “Journeys Out of the Body” sharing his experiences. He later created one of the first audio entrainment companies called Hemi Sync, alongside the Monroe Institute of Applied Sciences.
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.
Laughter releases endorphins that improve mood and decrease levels of the stress-causing hormones cortisol and adrenaline. Laughing tricks your nervous system into making you happy. Our suggestion: watch some classic Monty Python skits like “The Ministry of Silly Walks.” Those Brits are so hilarious, you’ll soon be cracking up, rather than cracking up.
Think about it for a moment...your mind is at work all day, every day. Every decision you make, every challenge that you face, every moment you go through in life, your mind is your constant companion, and it can be your best friend or your worst enemy. Your mind is something you need to take good care of, because your quality of life is directly related to your "quality of mind".
But the question is: Does it have a special effect on the brain? A lot of people think so. The basic claim being made for binaural beats is "resonant entrainment". Entrainment, in physics, is when two systems which oscillate at different frequencies independently are brought together, they synchronize with one another, at whatever the combined system's resonant frequency is. Examples of entrainment occur in animals in nature; for example the chirping of crickets or the croaking of frogs. Synchronization of menstrual cycles in women is another example. Even people coming together and dancing with one another is a type of entrainment. The basic claim for binaural beats is that the perceived low-frequency beat will entrain your brain wave pattern, thus forcing your brain into some desired state.
So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.
American Heart Association: "Four Ways to Deal With Stress."; PubMed Central: "Psychosocial and Psychophysiological Effects of Human-Animal Interactions: The Possible Role of Oxytocin."; NIH News in Health: "Can Pets Keep You Healthy?"; Cleveland Clinic: "Want a Healthy Heart? Laugh More!"; "Laughter Is the Best Medicine."; Association for Psychological Science: "Power Posing: Brief Nonverbal; Displays Affect Neuroendocrine; Levels and Risk Tolerance."; Harvard Business School: "Power Posing: Fake It Until you Make It."; "The Effect of Sexual Activity on Wages."
Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.

Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.