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.
Your brainwave activity during sleep is largely distinct from your brain activity when you’re awake. (REM sleep is one exception to this—during REM, your brain is active in ways very much like when you’re awake.) During non-REM sleep, the slower, lower frequency theta and delta waves dominate, compared to the alpha and beta waves that are prominent when you’re alert and active.
One larger and more recent randomized and controlled trial looked at the use of binaural beats in 291 patients admitted to the emergency department at a hospital. The researchers observed significant decreases in anxiety levels in patients exposed to audio with embedded binaural beats compared to those who listened to audio without binaural beats or no audio at all (headphones only).
There’s a growing body of research suggesting that binaural beats can reduce different forms of anxiety, from mild to chronic. One especially interesting study looked at the effects of binaural beats on anxiety among patients preparing to undergo surgery—a life circumstance that is pretty anxiety provoking for most anyone. Over a period of six months, patients spent 30 minutes on the day of their surgery listening to binaural beats. Compared to patients who listened to a soundtrack that did not include binaural beats—and patients who received no “beats” therapy at all—the binaural beat listeners experienced significantly greater reductions in their anxiety levels.
The same can be applied to the auditory senses, instead of the visual. Think of when you walk around the city with a friend or relative, have you ever noticed that your steps end up synchronized? Or when you walk with music which just happens to have a walkable tempo, before you know it you’re walking to the beat! This is how some insomniacs get treated. Binaural beats or brainwave entrainment aims to naturally help you synchronize yourself to a desired state of mind.
So, what we’re doing is combining these two parts, the awakening of complete stillness and deep relaxation with the rhythmic sounds, and embedding all frequencies within the music from right at the upper limits of human hearing to the lower limits. There is multi-level entrainment within Journey—I’ve layered in everything I know about audio brainwave entrainment into this track. 
With regard to listening without headphones specifically, you might find it irritating if you are someone who suffers from motion sickness, depending on how the track is created. If you were listening to binaural beats, they really need headphones to work properly. If you are in a room and closer to one speaker you may not even hear binaural beats properly, and if sitting off centre in the room generally, that may have unsettled you if you have motion sickness as the tones try to form a beat in your head. If it was just a standard isochronic tones theta track that shouldn’t be irritating if you have motion sickness.
In the average person, the activity of one brain hemisphere is dominant over the other, called brain lateralization. This hemispheric imbalance leads us to experience the world in a black and white way, perceiving separation over connectedness. When brainwave entrainment is used to synchronize brainwave activity in both hemispheres simultaneously, a person can more easily integrate information from all parts of the brain and solve problems with greater intelligence and sensitivity.
In 1984 medical researcher Dr. Gene W. Brockopp published a paper making several conclusions of audio and visual entrainment (AVE). Such conclusions were that hemispheric synchronization caused by AVE is related to increased intellectual functioning, practiced use of AVE overtime leads to a cumulative effect, and AVE may result in the recovery of early childhood experiences.
Using new scanning techniques, neuroscientists have discovered that certain areas of the brain light up constantly in Buddhists, which indicates positive emotions and good mood. "We can now hypothesize with some confidence that those apparently happy, calm Buddhist souls one regularly comes across in places such as Dharamsala, India, really are happy,"
A therapy that slows brainwave activity, helping to produce low frequency waves, is likely to aid relaxation and sleep. But it’s not only lowering brainwave frequency that binaural beats may offer to sleep and relaxation. A small study (19 people) has found that exposure to binaural beats is associated with changes to three hormones important to sleep and well being:
The following is an example of binaural beats incorporated into an actual piece of music and had even made the headlines as “the most relaxing song ever”. The song is called “Weightless” and is composed by the band Marconi Union, reportedly in collaboration with sound therapists. The official explanation is that the track would start on 60 beats per minute and slowly but surely slow it down to 50.
To fall asleep we need to go from our normal waking state, to a relaxed theta, and then finally all the way to delta. Binaural beats are a scientifically proven way to speed up this process, so you get to the delta state quicker and as a result fall asleep faster. For more about the science of binaural beats, have a read of the article Fall Asleep Fast With Binaural Beats.
Brainwave Entrainment is the process of synchronizing the brain to specific frequencies and patterns embedded in audio tracks. These frequencies correlate to specific emotions, feelings, and even energy levels. Using nothing more than sound, Brainwave Entrainment can enhance creativity, change moods, and even alter behavior like sleep and energy levels.

Please note: When you take one earphone out, move it as far away from your ear as possible. With some headphones you may still be able to hear the pulsating sound if the removed headphone is still fairly close to your ear; this is because your brain can still detect the frequency vibration coming from the headphone. In addition, push the earphone that’s still on your ear tightly to your ear, while moving the other earphone as far away as possible.

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