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.
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. 
While a practical understanding of brainwaves has been around for as long as people have been singing, chanting, and drumming, a scientific view of the electrical activity inside the human brain was not published until 1924 when German psychiatrist Hans Berger developed a machine for sensing and recording activity in the brain by attaching small electrical sensors to the scalp of his patients and recording the resulting electrical activity. Berger’s inventions and discoveries were built upon the earlier work of Richard Caton who published animal studies on brainwave oscillations in 1875.

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]

“A quite different phenomenon results when stereophonic earphones are used and the signals are applied separately to each ear. Under the right circumstances beats can be perceived, but they are of an entirely different character. They are called binaural beats. . . . Binaural beats require the combined action of both ears. They exist as a consequence of the interaction of perceptions within the brain.”
The easiest way to meditate Reach the deepest levels of meditation Obtain clarity and insight Experience mind-still blissful peace Now you can quickly reach depths of meditation that would otherwise take years of practice to attain. Brain Sync s precision-engineered frequencies massage your brain into mind-still blissful states of peace. With this program 87% of research subjects who never meditated before were able to enter the theta state their very first session. Guided Meditation Kelly Howell guides you create your own inner healing sanctuary, a place where you can go to revitalize the very core of your being. You ll learn how to generate states of being that nurture your sense of self, your creativity, and the dynamic expression of your power in the world. Deep Meditation Completely free of spoken words, this program delivers a unique combination of brainwave frequencies that produce an extraordinary mind-awake/body-asleep state. Negative thoughts are dramatically swept away by brilliant flashes of insight and understanding as you experience untold depths of inner peace. Clinical studies show that theta meditation increases creativity, enhances cognition, deepens perception, aids in overcoming substance abuse, and awakens intuition. In just 30 minutes you ll reap the same powerful benefits meditation masters have documented for millennium. The results are profound. This 2-CD extra value package includes both Guided Meditation and Deep Meditation at a special price.
Scientists and clinicians use brainwaves to measure and understand the functioning of the brain. We typically can’t see them, but human brains have billions of neurons. These individual neurons connect to thousands of other neurons. And when brain activity happens, these neurons light up much the same way thousands of audience members do “the wave” in an arena.
Newberg, who was catapulted to center stage of the neuroscience-religion debate by his book and some recent experiments he conducted at the University of Pennsylvania with co-researcher Eugene D'Aquili, says he has a sense of his own spirituality, though he declined to say whether he believed in God because any answer would prompt people to question his agenda. "I'm really not trying to use science to prove that God exists or disprove God exists," he said. Newberg's experiment consisted of taking brain scans of Tibetan Buddhist meditators as they sat immersed in contemplation. After giving them time to sink into a deep meditative trance, he injected them with a radioactive dye. Patterns of the dye's residues in the brain were later converted into images.
This is something which will come to you with practice. For instance you may feel an energy around and inside you like you have shifted dimensions but are still there. Instead of thinking this is God, the Zone or whatever, think of this as your soul, you essence, your expanded pure light being. In this way you will begin to train yourself to find your identity in your expanded being and your internal identity. This is what we want - to let go of the idea that we are a limited ego.
"When these people talk of religious experience, they are talking of a meditative experience," said John Haught, a professor of theology at Georgetown University. "But religion is more than that. It involves commitments and suffering and struggle ­ it's not all meditative bliss. It also involves moments when you feel abandoned by God." "Religion is visiting widows and orphans," he said. "It is symbolism and myth and story and much richer things. They have isolated one small aspect of religious experience and they are identifying that with the whole of religion."
Participants were experienced practitioners of Acem Meditation, a nondirective method developed in Norway. They were asked to rest, eyes closed, for 20 minutes, and to meditate for another 20 minutes, in random order. The abundance and location of slow to fast electrical brain waves (delta, theta, alpha, beta) provide a good indication of brain activity.
Monaural beats have similarities to binaural beats, but the two separate frequencies are delivered through a pulse pattern and mixed before they reach the listeners ears, resulting in the advantage of being audible without stereo headphones. However, using stereo headphones intensifies the effectiveness of monaural beats and is recommended for the best effect. 
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.
I have purchased several brain entrainment CDs, all of which have cost far more than the one I am using from the EOC Institute. Without a doubt, your CD outperforms the other ones hands down. It is nice to know that there are companies out there that truly put the customer first instead of the “ALMIGHTY DOLLAR” Thank you so much for your excellent product. It is a big help.
According to the Wikipedia entry “(i)n acoustics a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies.” Further, a binaural beat is “… an auditory illusion perceived when two different pure-tone sine waves, both with frequencies lower than 1500 Hz, with less than a 40 Hz difference between them, are presented to a listener dichotically (one through each ear)”. If the two frequencies are, say, 5 Hz apart as in 500 and 505 Hz, then a third tone at 5 Hz will be heard in addition to the two pure tones. What this technique allows for is the creation of an apparent auditory signal that can be perceived and that is at a predictable frequency. In this way, relatively low frequencies can be generated that can be easily perceived and that can correspond to the common brainwave frequency bands. These are often categorized as delta (0.5 – 4 Hz), theta (4 – 7 Hz), alpha (8 – 12 Hz), and beta (13 – 16 Hz). You may find somewhat different ranges and bands other than these listed depending on the source you consult. It is also possible to produce flashes of light that can be administered within these frequency bands but there is some risk of inducing seizures in susceptible individuals. While the most common frequency range for inducing seizures is 15 – 25 Hz, unfortunately, the possible range is 1 – 65 Hz, which covers essentially the whole range of standard EEG frequency bands. This makes use of sound stimulation safer than visual or combined audio/visual stimulation. 
Some studies have found that binaural beats can affect cognitive function positively or negatively, depending on the specific frequency that’s generated. For example, a study of long-term memory found that beta-frequency binaural beats improved memory, while theta-frequency binaural beats interfered with memory. This is something for scientists to continue to examine closely. For people who use binaural beats, it’s important to understand that different frequencies will produce different effects.
Meanwhile, the therapeutic benefits of listening to sound and music is a well-established principle upon which the practice of receptive music therapy is founded. The term 'receptive music therapy' denotes a process by which patients or participants listen to music with specific intent to therapeutically benefit; and is a term used by therapists to distinguish it from 'active music therapy' by which patients or participants engage in producing vocal or instrumental music.[37] Receptive music therapy is an effective adjunctive intervention suitable for treating a range of physical and mental conditions.[38]

Pure tones played together interfere with each other when they are close in pitch but not identical. When each tone is sent to a different ear, there will not be any physical interaction between the waves, yet your brain still creates an interference inside your head: the so-called binaural beat. In order to create a binaural beat, each ear must receive its dedicated signal. Therefore, binaural beats only work through headphones.