Binaural-beat perception originates in the inferior colliculus of the midbrain and the superior olivary complex of the brainstem, where auditory signals from each ear are integrated and precipitate electrical impulses along neural pathways through the reticular formation up the midbrain to the thalamus, auditory cortex, and other cortical regions.[6]
Theta: This brainwave pattern is associated with deep relaxation and with some stages of sleep, including the lighter stages of non-REM (NREM) sleep. REM sleep itself is mostly composed of beta wave and other activity that’s similar to an alert, waking brain. Deep meditation produces theta waves, which are slower and lower frequency (between 5-8 hertz) than Alpha waves. That murky barrier between sleep and wakefulness, when you’re drifting in and out of sleep, and your thoughts feel dreamlike and difficult to remember? That’s a theta-dominant state of consciousness.
I have read something different about theta waves and learning languages. A University of Washington study tested students resting brainwave activity before learning French. They found that students with a higher amount beta/gamma and a lower amount of delta/theta activity were better at acquiring a second language. When you are dominant in theta, that is the lowest and most deeply relaxed awakened state you can be in. I think it would be much harder to really concentrate, fully understand and learn new information while in a theta state, so I would personally consider using theta while studying.
Brainwave entrainment through the use of binaural beats is a scientific method that helps you go from alert to relaxed to asleep within minutes by using a process to alter your brainwaves. Sounds like something straight out of a science fiction novel, but brainwave entrainment is a very real and very effective way to help you sleep. Your alertness is linked to the dominant frequency of your brainwaves. So if you’re feeling alert and focused, your brainwaves are in the beta frequency but if you’re feeling relaxed, they’re likely to be in the alpha state. To sleep, your brainwave frequency needs drop to a slow delta. This can be hard, especially after a busy day. Your brain stays alert, preventing you from relaxing. By using Binaural Beats, you can quickly induce the frequencies associated with sleep in your brain within minutes.  Scientists discovered that the brain synchronises itself to a dominant frequency. So by inducing a new lower frequency with binaural beats, your brain begins to lower its own frequency to match this new frequency. It’s a powerful technology that I’ve been using myself for years with very good results.
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.
Brain Wave Entrainment is any procedure that causes one's brainwave frequencies to synchronize with a periodic stimulus (sound, vibration or light) having a frequency corresponding to the intended brain-state (for example, to induce a trance, dreams, sleep or relaxation.) It is also called the Flicker-response because of how staring at a campfire or the flickering of a burning candle can lull you into a state of calmness and serenity. There was an extensive article on this phenomenon by Gerard Oster in Scientific American in 1973. It may sound novel, but in many ways, this is old tech.

Synchronized brain waves have long been associated with meditative and hypnogogic states, and audio with embedded binaural beats has the ability to induce and improve such states of consciousness. The reason for this is physiological. Each ear is "hardwired" (so to speak) to both hemispheres of the brain (Rosenzweig, 1961). Each hemisphere has its own olivary nucleus (sound-processing center) which receives signals from each ear. In keeping with this physiological structure, when a binaural beat is perceived there are actually two standing waves of equal amplitude and frequency present, one in each hemisphere. So, there are two separate standing waves entraining portions of each hemisphere to the same frequency. The binaural beats appear to contribute to the hemispheric synchronization evidenced in meditative and hypnogogic states of consciousness. Brain function is also enhanced through the increase of cross-collosal communication between the left and right hemispheres of the brain.
Hello Jason, this is an unusually thoughtful discussion. Thank you for all your expertise and your kind manner of presenting and moderating it. I’m wondering if you have any experience with this: ever since I’ve been exposed to theta wave music, without headphones, I have found it irritating. And this is in spite of the fact that when I was first handed a CD by someone I knew well and trusted he was so confident I’d love it It didn’t occur to either of us that I might not. This happened again recently, which is about 10 years later, when I heard it playing overhead at an acupuncture clinic. I felt restless and even irritated, unable to zone out, which is unusual for me, during the treatment. I realized that the quality of my irritation was similar to what I’d felt listening to that CD a decade ago.So I asked if it was theta wave music and she said yes. The acupuncturist said that some people, but a vast minority, really dislike the music. She said that the few people who dislike it are not simply neutral, but actively dislike it. And she also said, but most people like it a lot. I’m just wondering what kind of factors might be present that would make a person feel so irritated by this music?

The main point is, you can be asleep while listening to any of them, but you won't be awake to feel anything. If you fall asleep while a beta binaural beat is playing, you may start to get anxious and start sleeping restlessly, you may even have a bad dream. This is because too much use of the higher beta range is associated with anxiety and stress, it's the “fight or flight” response you will experience.

When tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception[1], the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.
Therefore we are very receptive to new technology products that promise to improve our lives, or solve previously difficult problems, because of some new scientific or technological advance. This has created, in a sense, a marketplace of consumers that expect to be dazzled with technobabble they don’t understand, backed by assurances of legitimacy by the citing of research and association with professionals or professional institutions, and offering significant benefits. We are all, in a sense, waiting for that next product to improve our lives, and many of us like to feel we are on the cutting edge – getting an advantage over others by being savvy early adopters.
Binaural beats are auditory brainstem responses which originate in the superior olivary nucleus of each hemisphere. They result from the interaction of two different auditory impulses, originating in opposite ears, below 1000 Hz and which differ in frequency between one and 30 Hz (Oster, 1973).For example, if a pure tone of 400 Hz is presented to the right ear and a pure tone of 410 Hz is presented simultaneously to the left ear, an amplitude modulated standing wave of 10 Hz, the difference between the two tones, is experienced as the two wave forms mesh in and out of phase within the superior olivary nuclei. This binaural beat is not heard in the ordinary sense of the word (the human range of hearing is from 20-20,000 Hz). It is perceived as an auditory beat and theoretically can be used to entrain specific neural rhythms through the frequency-following response (FFR)--the tendency for cortical potentials to entrain to or resonate at the frequency of an external stimulus. Thus, it is theoretically possible to utilize a specific binaural-beat frequency as a consciousness management technique to entrain a specific cortical rhythm.  
With brain wave entrainment technology, changing brain wave states is an instantaneous and effortless process. The 'periodic stimulus' can be sound, vibrations and/or light. We have found that we get the best results with blinking lights which are experienced through closed eyelids. This is only problematic for people with existing diagnosis of photo-induced epilepsy, as blinking lights can induce a seizure in them. The programs are enhanced with Deepak Chopra doing the narration along with holographic sound effects and original music composed and performed by Rudy Tanzi.
Brainwave entrainment also happens with the use of pulsating light, and visual and auditory stimuli are sometimes combined for additional effect and visual stimuli is used alone. Using brainwave entrainment techniques is safe for almost everyone, the exception being pregnant women and people who have seizure disorders who should check with their physician before using these methods.

I am fortunate to be working with Deepak Chopra, M.D., and Dr. Rudy Tanzi, co-authors of the bestselling book Super Brain, on a technology called Brain Wave Entrainment. Deepak is very well known, but Rudy is an amazingly interesting person as well. He is the Kennedy Professor of Neurology at Harvard Medical School and Vice-Chair of Neurology at Mass General Hospital. Rudy co-discovered three of the four original Alzheimer's genes and today runs the Alzheimer's Genome Project. He also plays the keyboards, including, at times, for Aerosmith. He is kind of a real life "Buckaroo Banzai."

♥ ← This set of tones with the bird calls from Aotearoa is keeping me awake while I finish an essay I've been working on for the past four days. Focus beats + sounds I associate with morning = wakefulness. Still craving the bed, but at least I'm not falling asleep at my desk. Thanks myNoise, without you I'd probably be listening to music and distracted.

You’ve heard me talk before about how sound can make a difference to sleep. Patients often tell me that they fall asleep to relaxing music, they seem to find it really helps them let go of active thoughts and quiet their mind—which, like yours probably does, tends to race from one thing to the next all day long (aka I can’t turn off my brain syndrome).

In order to understand brainwave entrainment you first have to understand something about brain waves and electroencephalograms (EEG). Neurons are cells that communicate with each other through electrical conduction. When a neuron fires it creates a small electrical and magnetic field. These fields are far too small to measure by placing electrodes on the scalp, or even on the surface of the brain. The only reason we can detect the electrical fields of the brain is because many neurons are firing together – in synchrony. All brain waves that are measured by an EEG, therefore, represent a large group of neurons firing together.

Just my FIRST session I felt like I successfully achieved a theta state of meditation….I came out of it feeling extraordinarily renewed and with this profound insight of “everything is going to be ok”….this was all from my FIRST session. I cant wait to continue this on a regular basis to see where it leads….one day I hope to achieve the deeper delta states…
Because of the way they are created, there may be a positive benefit from listening to binaural beats without considering the brainwave entrainment aspect, but I haven’t seen any research on that. I first discovered brainwave entrainment through binaural beats about 10 years ago now, but they didn’t do anything for me. So I’ve never been a regular user of them. I believe isochronic tones are a more effective way to produce hemispheric synchronisation because they produce a much stronger response in the brain
A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion: