Some research suggests that the benefits from brainwave entrainment can last a lot longer, and still be seen for some time after you've stopped using it.  Study participants have still maintained improved test scores a few weeks after the stimulation had ceased.  Research on the long-term benefits has so far been minimal though, so how long the effects last is still up for debate.

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.
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“.
LEARNING OBJECTIVE • Exercise can be an effective component of a stress management program, and all types of exercise can be beneficial for stress management. Exercise programs consistent with the current recommendations to improve health can be prescribed to manage stress. Fitness professionals should recognize that it might be necessary to refer a client to a psychologist or other health care provider to help develop strategies for managing stressors that produce chronic and acute episodic stress.
Beta brainwaves are next highest in frequency after alpha waves, occurring at 13 to 30 hertz. Beta brainwaves are what we experience every day as we are awake and using our analytic mind. Beta brainwaves are needed for concentrating on mental tasks, and when they are present for too long of a time, they lead to stress, anxiety, and even paranoia. Most people do not have trouble achieving beta brainwaves and in fact suffer from spending too much time in beta brainwave patterns. However, those with attention deficit disorder (ADD) who have problems focusing their attention can benefit from learning how to achieve and remain in beta brainwave states for longer amounts of time.
Thanks to e-mail, cell phones, and BlackBerrys, it seems like your job never ends. The increasingly blurry boundaries between work and home life leave us with less downtime than ever before (and in some cases, no downtime!). Advances in technology are a leading source of chronic stress, putting many of us in a constant state of alert. Not to mention the effect it has on family ties. A recent study published in the Journal of Marriage and Family found a link between the use of cell phones and pagers at home and increased stress, which spills over into family life. To make technology work for you, screen calls with caller ID or, better yet, limit your cell phone and e-mail use to working hours only. Can't kick the BlackBerry habit? Set a regular time you'll check it in the evening (say, after dinner), so you're not constantly disrupting home life to keep tabs on work. (The one exception: using your device to breathe with this anxiety-reducing GIF.)
When your thoughts start to spin out of control during a stressful moment, stop and reframe your thinking. “By your choice of perspective, you direct how your body will respond—in fight or flight, or in creative choices and solution-based responses,” says Lauren E. Miller, stress relief and personal excellence expert and the author of 5 Minutes to Stress Relief. If you’re stressed about something you fear happening, such as “I’m not going to get this project done and then my boss will fire me,” think instead of what a great opportunity it is to show your boss you’re a hard worker. “Resist the urge to cast yourself as the main character in dramas that have not even occurred,” Miller says. Also, instead of asking why something is happening, ask what you can do to fix it. “Asking ‘why’ pitches you in an endless loop of questions, whereas asking ‘what’ sets you into problem-solving mode,” says Deborah Serani, PsyD, award-winning author of Living with Depression and a psychology professor at Adelphi University. “Moving forward instead of being lost in the circle of worries and “whys” helps to reduce stress.” Try these simple mindfulness stress relievers.
You probably already know that sex is a great tension reliever, but have you officially thought of it as a stress-relieving practice? Perhaps you should. The physical benefits of sex are numerous, and most of them work very well toward relieving stress. Sadly, many people have ​less sex when their stress levels are high. Learn how to avoid this trap.
The advice “take a deep breath” may seem like a cliché, but it holds true when it comes to stress. For centuries, Buddhist monks have been conscious of deliberate breathing during meditation. For an easy three- to five-minute exercise, sit up in your chair with your feet flat on the floor and hands on top of your knees. Breathe in and out slowly and deeply, concentrating on your lungs as they expand fully in your chest. While shallow breathing causes stress, deep breathing oxygenates your blood, helps center your body, and clears your mind.
Another consideration of stress is whether it is acute or chronic. “Acute stress” is what an individual experiences at the time the stressor is encountered (4). The stress response is activated, and the body returns to homeostasis once the challenge of the stressor is removed or the person successfully manages the situation. For example, an individual on the way to an important meeting gets into a traffic jam and realizes she is going to be late; the stress response starts. When she calls her boss and learns that she can conference into the meeting while on the road, the stress response subsides with the resolution of the situation. When an individual experiences acute stress on a consistent basis, such as with overcommitting at work or constant worrying, it is referred to as “acute episodic stress” (4). Individuals who experience acute episodic stress often show signs and symptoms of stress (Table 1) that can negatively impact physical and psychological health. These individuals can learn how to change behaviors and manage their stress to prevent these consequences.
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.

Brainwave entrainment is a method which utilizes frequencies of the brain in order to bring about specific desired thoughts and behavior. In other words, brainwave entrainment is used to induce different brainwave states related to: enhanced focus, relaxation, sleep induction, meditation, etc. With the help of a specific stimulus, aural (audio), photic (visual) or the combination of the two, we naturally induce the brain to respond by synchronizing with the stimulus frequency; this is called the “frequency following response”. The assumption is that the human brain has a tendency to change its dominant Electroencephalography frequency (recording of electrical activity along the scalp) towards the frequency of a dominant external stimulus. This is why we also talk about “brainwave synchronization”.

“In order to get into a flow state, you have to calm a part of the brain, the posterior cingulate cortex, which is the source of what brain scientists call the default state, which is the non-focused state,” says Harris. “At any rate, it turns out that Holosync [binaural beats], when you listen to it, [calms that part of the brain] and so does traditional meditation. It’s just Holosync does it faster and more easily and more effortlessly. It turns down the posterior cingulate cortex and it enhances the other part of the brain that, when it’s enhanced, you can easily go into a flow state.”

Stress affects your whole body, so find a pick-me-up for each of your senses. Turning on a favorite tune uses your sense of hearing for a science-backed burst of good feeling, and using aromatherapy uses your sense of smell to relax you. “Oils like lavender and lemon reduce stress,” Dr. Serani says. “Also, don’t forget that your sense of smell is the most nostalgic of all your senses,” so if you have a scent that reminds you of comfort, keep it on hand to sniff when you’re freaking out. Your sense of touch can be employed by stroking a “talisman”—a favorite or sentimental item—or even an “intention stick,” which you can hold like a wand to feel more in control. Chew gum to use your sense of taste to curb stress (scientists think it’s the lasting flavor, not just the act of chewing itself, that makes gum such a great stress reliever). Besides using your mind’s eye to visualize a happy place, you can use your sense of sight to look at calming images—cat videos on the Internet have actually been scientifically proven to lower stress.
The most common way to use a brainwave entrainment is for a short-term benefit, to help guide your brain into a particular mental state at the time you need it.  In a similar way to how you might take a sleeping pill before bed to help you get to sleep, or maybe drink some coffee or an energy drink to help wake you up and give you a boost of energy.

Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).  
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.
Entrainment is a principle of physics which appears in biology, chemistry, neurology, medicine, astronomy etc. It is defined as the synchronization of two or more rhythmic cycles. In the seventeenth century, Dutch scientist Christian Huygens found out that by placing two unsynchronized clocks side by side on a wall, they would slowly synchronize to each other in a very accurate way. The clocks were the first example of spontaneous synchronization, a phenomenon found throughout nature from cells to the Solar System.
Entrainment guides our brainwaves into targeted ranges, but they are ranges we go through naturally many times every day. LifeFlow 10, for example, takes the brain to a 10Hz frequency. We experience this same frequency when closing our eyes and taking a deep breath, or when consciously relaxing physical tension in the body, or when we find ourselves lost in a daydream, or when we view a beautiful sunset, or when we find ourselves caught up in an especially peaceful bit of music. If there was a cause-and-effect relationship between these 10Hz brainwaves and our face flushing, then our face should also flush when we enter that daydream, listen to that piece of music, watch that sunset, or close our eyes and relax. The same brainwave patterns are present during all those activities as they are while listening to LF-10. But these other activities don’t bring on the same face flushing.

Also, don’t you think that the inherent hemispheric synchronization using binaural beats might be a positive benefit within itself? While it’s true that the huge majority of us use both sides of our brains most of the time, it’s also true that many of us are a bit polarized to one side or the other in general, or when doing a particular kind of activity or focus. I’ve found stimulating a more equally and consistently whole brain activity has it’s own benefits other than the entrainment aspect.

When your thoughts start to spin out of control during a stressful moment, stop and reframe your thinking. “By your choice of perspective, you direct how your body will respond—in fight or flight, or in creative choices and solution-based responses,” says Lauren E. Miller, stress relief and personal excellence expert and the author of 5 Minutes to Stress Relief. If you’re stressed about something you fear happening, such as “I’m not going to get this project done and then my boss will fire me,” think instead of what a great opportunity it is to show your boss you’re a hard worker. “Resist the urge to cast yourself as the main character in dramas that have not even occurred,” Miller says. Also, instead of asking why something is happening, ask what you can do to fix it. “Asking ‘why’ pitches you in an endless loop of questions, whereas asking ‘what’ sets you into problem-solving mode,” says Deborah Serani, PsyD, award-winning author of Living with Depression and a psychology professor at Adelphi University. “Moving forward instead of being lost in the circle of worries and “whys” helps to reduce stress.” Try these simple mindfulness stress relievers.
A large dose of caffeine causes a short-term spike in blood pressure. It may also cause your hypothalamic-pituitary-adrenal axis to go into overdrive. Instead of coffee or energy drinks, try green tea. It has less than half the caffeine of coffee and contains healthy antioxidants, as well as theanine, an amino acid that has a calming effect on the nervous system.
Building on guided imagery, you can also imagine yourself achieving goals like becoming healthier and more relaxed, doing well at tasks, and handling conflict in better ways. Also, visualizing yourself doing well on tasks you’re trying to master actually functions like physical practice, so you can improve your performance through ​​visualizations as well.
Experts haven't figured out why having your body pressed and prodded works wonders, but they know that it does. Studies suggest massage can speed up weight gain in premature babies, improve lung function in asthmatics and boost immunity in men with HIV. If you can't indulge in regular full-body massages, treat yourself to the occasional pedicure, manicure or facial—all nurturing, hands-on treats that offer some of the mind-body benefits of massage. 
A simple spinal twist can help you get a better night's sleep. It alleviates tension that's built up in your lower back throughout the day. Sitting on your bed with legs crossed, place your right hand down on the bed behind you and rest your left hand on your right knee. Sit up straight and inhale for four to eight counts, lengthening your spine as you breathe. On your exhale, begin to twist toward your right hand (don't strain your neck). Hold this position for four more full breaths, lengthening your spine on the inhales and deepening your twist on the exhales, if it feels comfortable. Repeat yoga asanas on opposite side. (These stress-reducing yoga poses also help calm anxiety.)
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.
When you hit a tuning fork, tuned to a particular sound frequency such as the note B, and hold it close to the strings of a guitar, you will notice that the B string on the guitar will vibrate because it has entrained on to the same frequency of the tuning fork. Interesting enough, the other strings will not vibrate. Only the one with the same tuning as the tuning fork.

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)
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