You don't have to buy one, though. It's not too hard to make your own binaural beat, and free software is widely available to do just that. The one that I used to make that little sample is an open-source program called Gnaural, available on the Sourceforge website. It's pretty easy to use, though it takes some practice before you can generate some of the really cool, more professional sounding beats. A binaural beat consists of two simple tones, and most people add that background pink noise. Nothing special.
There were no significant differences between the experimental and control conditions in any of the EEG measures. There was an increase of the Profile of Mood States depression subscale in the experimental condition relative to the control condition (p = 0.02). There was also a significant decrease in immediate verbal memory recall (p = 0.03) in the experimental condition compared to control condition.
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In 1973, biophysicist Dr. Gerald Oster published a famous article in Scientific American titled “Auditory Beats in the Brain”, which found that when two pure tones of varying frequencies were combined, a third rhythmic beat was created which he called binaural or monaural beats. According to Oster, monaural beats occur when two tones are combined and sent through a loudspeaker, while binaural beats occur when stereo headphones are used to deliver each tone separately to each ear. Oster concluded that monaural beats were a more effective form of brainwave entrainment.
In one study, researchers had a group of participants relax alone in a quiet, low-light environment following an exercise session. They split the group in two — one spent 20 minutes listening to theta-frequency binaural beats while the other listened to a carrier tone and monitored their parasympathetic (rest and relaxation) and sympathetic (fight or flight) nervous system activity. Researchers found the group that listened to binaural beats experienced an increase in parasympathetic activity and a decrease in sympathetic activity, along with higher rates of self-reported relaxation.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself. 

Go behind the scenes of brainwave entrainment technology creation with Joseph Kao, developer of the extraordinary meditation tool Journey to the Center of the Self. Here, in an interview with John Dupuy, CEO of iAwake Technologies, Joe describes the amazing complexity of the brainwave entraining soundscape he created to both accompany his deeply inductive, 30-minute, guided meditation on the first track of Journey, and also stand alone as a music-only track that holds you in a profoundly relaxed, still, yet clear place on the theta/delta border. To find out all that went into the making of the inductive guided meditation on the first track of Journey, see A Guide to Transpersonal Meditation: Journey to the Center of the Self, part I of this interview.

Controlled or pre/post studies of the effects of BWE using auditory or visual stimulation were eligible for inclusion, provided pulses of light or tone were delivered at frequencies hypothesised to have a beneficial effect or in line with a protocol addressing clinical outcomes. Studies were required to report clinical or psychological outcomes (measured using standard methods or as deemed appropriate by peer review) and to report statistical analysis. Studies of outcomes such as electroencephalogram (EEG) response or neurotransmitter levels were not eligible. Case studies were excluded.
For example, if a 530 Hz pure tone is presented to a subject's right ear, while a 520 Hz pure tone is presented to the subject's left ear, the listener will perceive the auditory illusion of a third tone, in addition to the two pure-tones presented to each ear. The third sound is called a binaural beat, and in this example would have a perceived pitch correlating to a frequency of 10 Hz, that being the difference between the 530 Hz and 520 Hz pure tones presented to each ear.
Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.
“Like the pulses of vibration that produce sound on a guitar string, your brain also creates pulses of vibrations. These vibrations are electrical impulses,” continues Naik. “Their activity can be measured by using an EEG (electroencephalogram), which measures the frequency of these pulses [which is measured in Hertz]. Your brain actually has a predominant frequency at which it operates in any given moment; this can be associated with your state of mind.”
Brain research is beginning to produce concrete evidence for something that Buddhist practitioners of meditation have maintained for centuries: Mental discipline and meditative practice can change the workings of the brain and allow people to achieve different levels of awareness. Those transformed states have traditionally been understood in transcendent terms, as something outside the world of physical measurement and objective evaluation.
This simple app doesn’t have tons of bells and whistles, but by being just a one-screen app it doesn’t drain your battery or interfere with other apps you might be running. The interface is straightforward and lets you input exactly what binaural beats frequency you want to achieve. This is a great app if you know exactly what you want and you don’t want anything to get in the way of that.

a concise P.S. I was in a horrible car accident when I was 18 and had to learn to read and write and walk and talk all over again. It was long ago and I’m pretty well over it, but such an injury has lifetime repercussions. The neurological damage sustained causes my left arm to shake uncontrollably anytime I use it in a situation requiring precise coordination. From simply listening to the demo, the shake [though not disappearing completely in the last 2 months] has lessened dramatically. I had been wondering for years what kind of neurological exercises I could undergo to help it…

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.

You may recognize the "binaural recording" from ASMR, where the technique is often used. This explains why, if you search for "binaural" on YouTube, you get a mixture of two entirely different kinds of results: binaural beats and binaural ASMR recordings. It gets especially confusing in that there's some questionable and/or unexplored science surrounding each one.
When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  
Binaural beats can easily be heard at the low frequencies (< 30 Hz) that are characteristic of the EEG spectrum (Oster, 1973). This perceptual phenomenon of binaural beating and the objective measurement of the frequency-following response (Hink, Kodera, Yamada, Kaga, & Suzuki, 1980) suggest conditions which facilitate entrainment of brain waves and altered states of consciousness. There have been numerous anecdotal reports and a growing number of research efforts reporting changes in consciousness associated with binaural-beats. "The subjective effect of listening to binaural beats may be relaxing or stimulating, depending on the frequency of the binaural-beat stimulation" (Owens & Atwater, 1995). Binaural beats in the delta (1 to 4 Hz) and theta (4 to 8 Hz) ranges have been associated with reports of relaxed, meditative, and creative states (Hiew, 1995), and used as an aid to falling asleep. Binaural beats in the alpha frequencies (8 to 12 Hz) have increased alpha brain waves (Foster, 1990) and binaural beats in the beta frequencies (typically 16 to 24 Hz) have been associated with reports of increased concentration or alertness (Monroe, 1985) and improved memory (Kennerly, 1994).

Brainwave entrainment is a method to alter the frequency of your brainwaves by listening to audible tones containing the desired frequency. So if you want to sleep, you would listen to audio that begins at your current frequency and slowly descends to a delta frequency. By introducing these new lower frequencies, your mind begins to lower its own brainwaves to match this new frequency.
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.
Jeffrey D. Thompson, D.C., B.F.A. Disclaimer: Nothing on this website is intended to diagnose, treat, cure or prevent any medical condition of whatever nature, and shall not be construed to mean medical advice, implied or otherwise. Information on this site is intended for educational edification and use only. © Coyyright 1988-2018 – Center for Neuroacoustic Research - All Rights Reserved.
Other research by Paul Ekman, of the University of California San Francisco Medical Center, suggests that meditation and mindfulness can tame the amygdala, an area of the brain which is the hub of fear memory. Ekman discovered that experienced Buddhists were less likely to be shocked, flustered, surprised or as angry as other people. Flanagan believes that if the findings of the studies can be confirmed they could be of major importance.

Theta also plays an important part in behavior modification programs and has been used in the treatment of drug and alcohol addiction. Because theta brainwave activity induces an "endorphin high" it can reduce the desire for mind altering substances. Also, because theta is associated with heightened receptivity, it is the ideal state to reprogram your mind with positive thoughts that assist in changing habits and behaviors.
^ Jump up to: a b Fox, Kieran C.R.; Nijeboer, Savannah; Dixon, Matthew L.; Floman, James L.; Ellamil, Melissa; Rumak, Samuel P.; Sedlmeier, Peter; Christoff, Kalina (2014). "Is meditation associated with altered brain structure? A systematic review and meta-analysis of morphometric neuroimaging in meditation practitioners". Neuroscience & Biobehavioral Reviews. 43: 48–73. doi:10.1016/j.neubiorev.2014.03.016. PMID 24705269.
Go behind the scenes of brainwave entrainment technology creation with Joseph Kao, developer of the extraordinary meditation tool Journey to the Center of the Self. Here, in an interview with John Dupuy, CEO of iAwake Technologies, Joe describes the amazing complexity of the brainwave entraining soundscape he created to both accompany his deeply inductive, 30-minute, guided meditation on the first track of Journey, and also stand alone as a music-only track that holds you in a profoundly relaxed, still, yet clear place on the theta/delta border. To find out all that went into the making of the inductive guided meditation on the first track of Journey, see A Guide to Transpersonal Meditation: Journey to the Center of the Self, part I of this interview.
The aim of this study is to identify tendencies in the effectiveness of relaxing audio stimuli that could be verified through further focused experiments. A series of brainwave entrainment (BWE) techniques for inducing relaxation will be presented consisting of different binaural phenomena (BP). The BP will derive from the binaural sine wave beat, widely acknowledged in rhythmic BWE... [Show full abstract]
Eric Bartel is the creator of the Free Binaural Beats website and the sole creator of the audios found here. He specializes in creating binaural beats and isochronic tones along with relaxing ambient meditation music. From his home studio in the Black Hills of South Dakota, Eric is committed to bringing the healing power of binaural beats to anyone who wants to live a more peaceful, relaxed and fulfilled life.
As the ancient cultures believed that sound waves of different frequency and beats could induce a state of meditation. Ancient Hindus and Yogis believed that specific kind of sound waves can induce relaxing effects. I found the best binaurial beat app BINAURAL BEATS - MEDITATION & RELAXATION - Apps on Google Play as it is designed to provide you with the best meditation, deep sleep, stress relief, healing and sleep sounds.
A study by Tina Huang, PhD, and Christine Charyton, published in the September 2008 issue of the journal, Alternative Therapies examined the results of twenty previous studies measuring the effectiveness of brainwave entrainment for improvements in cognitive dysfunction and deficits, stress reduction, pain management, migraine and headache control, pre-menstrual syndrome, and behavioral difficulties, and all showed significant improvement in symptoms using entrainment techniques.
When I am using equisync I feel kind of like it is “pushing me” – I guess this is the right way to say it- to achieve better results, which I really like. I fall asleep quickly, and sleep all night and even wake up before my alarm goes off. I feel noticeably calm during the workday- which is very helpful for what I do. I really like the warm feeling (my whole body gets really warm during my equisync meditation sessions) and I feel kind of like Im floating while listening. The soothing rainfall is also very nice.

♥ I've beeen training in self-hypnosis for a while (under supervision and for a reason) and found that the 8-4 Hz beats put me very quickly in a deeply relaxed state. Definitely the thing! With the timer, I can shut them for the real self-hypnosis. I haven't tried the other beat generators yet, but this one works much better than I expected and clearly does the job. In a few words: I'm impressed!