Rudy's primary work is on Alzheimer's. In this disease, beta amyloid proteins form plaques in the brain and kill nerve cells eventually leading to dementia. Research from Washington University School of Medicine in St. Louis shows that when people's brains are in a Delta brain wave state, beta amyloid production in the brain ceases and the toxic material is cleared away. One thought is to explore the possibility of using brain entrainment technology to help treat Alzheimer's, but at this point all it is being used for is to help people meditate, relax and dream instantly and effortlessly.
So, in summary, binaural beats certainly do not work the way the sellers claim, but there's no reason to think they're any less effective than any other music track you might listen to that effects you in a way you like. If they make you sleepy (like they all do for me), use them to go to sleep. If they relax you or get you amped, use them for that. But don't expect them to be any more effective than regular music. If someone you know claims that they are, put them to the test, and bust the myth.
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)
Brainwave Entrainment is an assisted form of meditation using pulses of sound. Entrainment is a process of synchronizing two different beats to become harmonious. Brainwave entrainment works by pulsing a different sound in each ear to stimulate the brain into altered states of consciousness. Examples including Binaural Beats and Isochronic Tones, which are best experienced with headphones to assist with relaxation, deep sleep and focus.

A popular opinion in the brainwave entrainment community is that listening to isochronic tones without music produces a much stronger effect.  However, in the study by Doherty, Cormac. “A comparison of alpha brainwave entrainment, with and without musical accompaniment” (2014),  it was concluded that brainwave entrainment was equally effective for isochronic tones, both with and without music.
Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.
Your brain cells reset their sodium & potassium ratios when the brain is in Theta state. The sodium & potassium levels are involved in osmosis which is the chemical process that transports chemicals into and out of your brain cells. After an extended period in the Beta state the ratio between potassium and sodium is out of balance. This the main cause of what is known as "mental fatigue". A brief period in Theta (about 5 - 15min) can restore the ratio to normal resulting in mental refreshment.  
Beware simple answers to complex problems, or easy methods for accomplishing difficult goals. If you combine this maxim with the advice to be skeptical of any claims that are being made in order to sell you something – then ironically you have a simple method (perhaps I should call it an “elegant” method) for protecting yourself from most scams and cons. Actually the application of this combination of maxims can be complex, but what it does do is trigger doubt and skeptical analysis. (And to be clear I am not saying that all simple solutions must be wrong – you should just beware them, meaning your skeptical senses should be tingling.)
Sleep issues are becoming much more of a common problem. I think it's great to look at alternative ways to help with insomnia and other sleep related issues, especially when they don't involve the need to take medication. Something proved to be effective is 'Sleepstation' a UK based organisation who use CBT techniques to cure insomnia. Their online sleep therapy course is brilliant and very convenient as it's delivered online. Their website is definitely worth a look if you're having sleep issues
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.
With digital upgrades, Berger’s machine is still in use today, known as an electroencephalography machine, or EEG. Berger used his machine to study the brains of psychologically normal and abnormal people and discovered the first brainwave, called the alpha wave and also known as the Berger wave, along with the faster beta wave, which he observed suppressing the alpha wave when subjects opened their closed eyes. 
... One of the possible explanation for insignificant results could be length of exposure to AVS. Our participants were exposed to it for 11 minutes, while some authors (Cruceanu & Rotarescu, 2013) suggest that at least 20 minutes is needed for the positive effects to take place. Furthermore, part of our reserach was also visualization of gymnastic skills, performed after AVS. ...
Just as stress can increase the risk for chronic diseases and other health problems, dealing with chronic conditions and poor health can increase the amount of stress one experiences. Stress also influences behaviors that affect health. Diet choices, sleep habits, and drug use are behaviors that are often negatively affected by stress (3). The APA’s 2011 survey showed that 39% percent of respondents reported overeating or eating unhealthy food because of stress, and 29% reported skipping a meal (3). In addition, 44% reported lying awake at night because of stress (3). On a positive note, 47% of respondents reported walking or exercise as a way of managing stress (3).
Researchers advise that people who suffer from epilepsy or seizures should ask for professional insight first before using binaural beats. Pregnant women are also advised to seek the advice of their physicians. However, I haven’t heard anything about binaural beats impacting those who have had heart attacks negatively. That being said, I encourage you to do extra research.
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.
Writing or talking about the things that prey on you—in a diary, with friends, in a support group or even a home computer file—helps you feel less alone and helpless. One study, published in The Journal of the American Medical Association, looked at people who had either rheumatoid arthritis or asthma— conditions known to be stress-sensitive. One group chronicled in a perfunctory manner the things they did each day. The other group was asked to write daily about what it was like, including fears and pain, to have their disease. What researchers found: People who wrote at length about their feelings had far fewer episodes of their illness.
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.

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.
Hey, even before we spoke about creating Journey, I was thinking about how people across the world do their spiritual practices and the commonalities between them all. I was thinking, there is the path of stillness—which links right back to what we were talking about getting to a state of deep, profound relaxation and bringing clarity into stillness. Then there’s the path of rhythm, of rocking, of dancing. But there’s always a rhythm to it—even in the movements of Tai Chi, there’s a smoothness, a smooth rhythm. What it never is, is arrhythmic—those are the movements of a more anxious, frightened animal kind of thing. 
Now you are ready to experience Delta with the Theta & Delta Deep Meditation tracks. These two tracks work together the same way the Alpha/Theta recordings do. If you have a full hour, definitely use both of these tracks together, starting with Theta Deep Meditation first. The combination of these two tracks is extremely powerful and will give you maximum benefit to your mind, body and emotions.
... [9] While entrainment by binaural auditory beats in the alpha frequency has also been shown to enhance creativity, cognition, memory, and an improvement in intelligence tests and achievement tests in learning disabled boys. [10][11][12][13] The gamma-band activity has been shown to involve in a variety of functions such as attention, memory, and consciousness. Current literature suggests that entrainment by gamma beats promotes cognitive flexibility, modulates visual attention, and enhances creativity. ...

Several adaptogenic herbs and essential oils have been shown to improve anxiety symptoms by reducing the effects that stress and cortisol have on the body. Adaptogens (including ginseng, ashwagandga, maca, rhodiola, holy basil and cocoa) are a unique class of healing plants that balance, restore and protect the body and make it easier to handle stress by regulating hormones and physiological functions.
The Frequency following response (FFR), also referred to as Frequency Following Potential (FFP), is a specific response to hearing sound and music, by which neural oscillations adjust their frequency to match the rhythm of auditory stimuli. The use of sound with intent to influence cortical brainwave frequency is called auditory driving,[39][40] by which frequency of neural oscillation is 'driven' to entrain with that of the rhythm of a sound source.[41][42]