Alpha (12hz – 8hz) – Awake, but deeply relaxed. Simply closing your eyes will produce alpha brainwaves. This category is associated with daydreaming, visualization, imagination, light meditation. Brainwave expert Anna Wise called the alpha range the bridge between beta and theta. (More information can be found in Wise’ book The High-Performance Mind)

“Binaural beats” are a specific kind of sound that can shape your brain activity to boost your concentration, enhance your creativity, and improve your mood. Listening to binaural beats is a free, safe, and increasingly popular way to help maintain good mental health. Read on to learn more about binaural beats and how they can be used to improve your mental clarity and health.
A few years ago I was very sick with anxiety. I saw a Psychologist and he recommended the Audio Deep Sleep. I was uncertain at first and falling asleep with the sound sounded odd at first. As I progressed, I became at one with the CD and soon found, if I missed a night I soon missed playing the CD. Over the course of time I have done quite a bit of healing and found I was not using the CD much. Over the past few months I really missed it and found the CD hard to find. It wasn't until I happened upon this site and found the Deep Sleep CD. I played the sample and found myself missing the CD greatly and discovered my brain seemed to miss it just as much. I am grateful to you and just as much as my Doctor has given me my life back to a fair extent, I am am grateful to you as well. :)
Generally speaking, the brain will usually entrain to the strongest stimulus which would be isochronic tones over binaural beats. So when you see people add binaural beats at a different frequency to the isochronic tones, that would not produce additional brainwave entrainment at another frequency. If they are both at the same frequency I haven’t seen any research to indicate whether that would be beneficial or not, but my belief is that it would weaken the potential for entrainment. When you look at the waveform of an isochronic tone there is a distinct empty space between each beat, making it very pronounced and effective. When you add binaural beats at the same frequency it looks like this: The depth of the waveform is now half as deep and less effective. This is before the binaural beats are formed inside your head, where the waveform is hard to determine and measure. From listening to that type of combination the beats sound much less pronounced, which has to make them much less effective in terms of a brainwave entrainment stimulus, compared to isochronic tones on their own.
The name of the game (and by game, we mean mind hack) is binaural beats. Binaural beats refer to the event in which two similar — but not identical — frequencies are played in different ears through headphones. For example, you might have a 300 Hz tone playing into your left ear, and a 305 Hz tone playing into your right ear (hence the need for headphones, since it’s important for the different sounds to be heard in isolation). Your brain will hear those two tones, yes, but what it will also pick up a 5 Hz tone – the difference between the two frequencies – which is actually too low for our ears to hear. So what’s happening here is not that your ears are suddenly picking up a tone that they couldn’t prior, but instead, your brain is producing the tone; you are perceiving it, not actually hearing it. The resulting noise that you will hear is a steady rhythm, about 4.5 beats per second. Your brain, in the process, will actually emit brainwaves at the frequency of the synthesized tone.
Back in 1839, Dr. Heinrich Wilhelm Dove, a Prussian physicist and meteorologist, discovered that when you introduce tones with certain frequencies into each ear, you could actually entrain the electrical patterns within the brain to resonate in very specific patterns, called brainwave states. The last two decades have seen an amazing amount of scientific interest in this world transforming field of study, laying the foundation for the hundreds of studies conducted since then, boosting the technology’s significance and importance immeasurably.
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At the end of just two weeks of use (I was now into the Equisync II cds), I experienced for the first time ever, what my partner described as Nirvana. I experienced a complete dissolution of individual consciousness, felt at one with everything, and felt the deepest peace, love, and complete bliss I had ever, ever experienced in my life. Since you do all the research on this, you know what I’m describing. Unfortunately, language does not express it. I have never experienced mind altering drugs, but I recall watching a documentary of LSD research, and one of the subjects described the exact same “feelings” as I had when she had received a micro amount of LSD.
All you need to experiment with binaural beats is a binaural beat audio and a pair of headphones or earbuds. You can easily find audio files of binaural beats online, such as on YouTube, or you can purchase CDs or download audio files directly to your mp3 player or other device. As mentioned earlier, for a binaural beat to work, the two tones have to have frequencies of less than 1000 Hz, and the difference between the two tones can’t be more than 30 Hz.
Binaural beats work by playing a different tone in each ear, and in the process the brain creates a “phantom tone” which is the difference between the two tones (for example if you play a 300 hz tone in one ear and a 310 hz in the other ear the brain will produce a 10 Hz phantom tone.) If this phantom tone is 10 hz the brain will gradually be led to a dominant brainwave frequency of 10 hz (this has been measured by EEG devices). If the tone is 7 hz the brain will gradually be led to a 7 hz dominant frequency, and so on.

When you listen to binaural beats/tones, you are actually listening to two slightly different pitched frequencies. Each frequency goes to each of your ears independently. When this happens your brain responds by creating a third tone, making up the difference between the two frequencies. This shift in frequency then shifts your brain’s consciousness and changes your state.

The binaural-beat appears to be associated with an electroencephalographic (EEG) frequency-following response in the brain (3). Many studies have demonstrated the presence of a frequency-following response to auditory stimuli, recorded at the vertex of the human brain (top of the head). This EEG activity was termed "frequency-following response" because its period corresponds to the fundamental frequency of the stimulus (Smith, Marsh, & Brown, 1975). Binaural-beat stimulation appears to encourage access to altered states of consciousness.

As to the second question raised in the above paragraph, audio with embedded binaural beats alters the electrochemical environment of the brain. This allows mind-consciousness to have different experiences. When the brain is entrained to lower frequencies and awareness is maintained, a unique state of consciousness emerges. This state is often referred to as hypnogogia "mind awake/body asleep."  
This phenomenon is best known in acoustics or music, though it can be found in any linear system: "According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes".[2] If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant as when a pure note is played, but change over time: when the two waves are nearly 180 degrees out of phase the maxima of one wave cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the perceived volume.

Isochronic tones work by influencing your brainwave activity and they can’t directly affect the body. That said, the brain does control the body, so sensations and feelings can sometimes be felt in the body after stimulating your brainwave activity. Some people who are new listeners of this type of audio can sometimes feel tingling sensations in their body. Not everyone feels this and these sensations usually stop once you get more used to using the audios. Isochronic tones are considered as a safe technology. However, sometimes they can leave you feeling temporarily fatigued, especially if you listen to them for an extended period (hours) when you first start using them. If you felt fatigued, I would recommend using them for a much shorter period while you are getting used to them and ensure you are well-hydrated.
These sounds in these musical tracks are presented through monaural beats, binaural beats, isochronic tones, or a mixture involving combinations of all three of these modalities, described in detail below. Choose alpha brainwave tracks for calming anxiety and relaxing body and mind, and choose theta tracks for help in getting to sleep and for bringing hidden feelings to the surface. Some people also report out-of-body type experiences when in theta brainwave states.
There are five main categories of brainwave frequencies: Gamma (40Hz+), Beta (13 – 40Hz), Alpha (7 – 13Hz), Theta (4 – 7Hz), and Delta (<4Hz). Each category is associated with a different state of mind; so, for example, when you’re in a peak state of performance, your brain produces Alpha Waves, and when you’re in a deep sleep, your brain produces Delta Waves.
While originally brainwave entrainment was achieved by using pure tones of sound, it is now possible to take these tones and blend them with music, rhythms, and natural sounds, such as the sounds of flowing water, bird sounds, or waves lapping on a beach, creating extended tracts of varied and intriguing brainwave entrainment music for everyday use.
But we don't need any studies to tell us that different people can listen to different kinds of music and be affected. A lot of people who work out have a workout playlist on their iPod that keeps them energized. Some people listen to certain music to help them fall asleep. The Muzak company has built an industry on relaxing music that will keep people in the mood to shop. Music does affect our mood, and so we already have every reason to expect binaural beat recordings to produce the same effect. Different people may find certain binaural beats to be relaxing or energizing. But, we've never found any reliable indication that a binaural beat's connection to our brain is any deeper or more meaningful than any other music track. We do know for a reasonable certainty that specific claims made by most sellers of binaural beats are not credible, and that there is no reason to think that the effect they're claimed to produce will work for you.