Cortisol is an arousal hormone, stimulating alertness and attention. Cortisol levels rise and fall in connection to circadian rhythms—cortisol levels rise to their peak levels first thing in the morning, just in time for you to be active for the day. Too-high cortisol levels are associated with insomnia, as well as more time spent in light sleep, rather than deep sleep.
♥ ← This set of tones with the bird calls from Aotearoa is keeping me awake while I finish an essay I've been working on for the past four days. Focus beats + sounds I associate with morning = wakefulness. Still craving the bed, but at least I'm not falling asleep at my desk. Thanks myNoise, without you I'd probably be listening to music and distracted.
Binaural beats are acoustically generated frequencies that match the frequency bands of brain waves and are therefore considered a means to inducing neurophysiological relaxation. There is, however, large dispute on the scientific quality and validity of extant research on binaural beats. Thus, the effect of a binaural 10Hz (Alpha) stimulation on subjective and physiological parameters... [Show full abstract]
I’ve been using equisync first thing in the morning after I get up, and listen to all three tracks in a row. I again listen to all three tracks in the late afternoon. If I don’t have that much time available, I will start on Track 2 or 3, as necessary. I have really started to focus on my breathing, and notice the difference – I finish the session in a DEEPLY relaxed state.

Listening to binaural beats is not something to be feared, however. In most situations, listening is safe and very enjoyable. Choosing a track from various websites online, as well as some videos on YouTube.com, can assist you in relaxing and can bring about a more restful sleep. Choosing a Beta entrainment can help with alertness and focus, while listening to an Alpha wave track can help you to relax and learn new information. Theta tracks can help to change some negative emotions, or to help you drift off to a sounder sleep. Delta waves will help to accelerate healing. To use them, you must use headphones or earphones, because each ear will hear a different frequency. You should make the commitment and listen daily; consistency is key in order to achieve maximum benefits. However, please don't listen to binaural beats twenty four hours a day; once daily for a short period of time is perfectly fine. You should also make yourself comfortable; either lying down or sitting in a comfortable chair will help you to relax. You can do them right before sleep, or right upon awakening. Listening during meditation or visualization exercises will help to improve and deepen your practice. If you feel a little blue or you need a break from the daily routine, you can pop a CD in and unplug completely. When you return to whatever you were doing, you will find that you are more refreshed and ready to take on whatever is before you.
Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.

The effects are strongest while you are listening to the tones because your brainwaves are synchronized and tuned into the frequency range you desire at that time.  After you've stopped listening the effects can still linger for a while afterwards.  The timescale will vary from person to person and be affected by what you do after you've stopped listening.

When blended with musical sounds, brainwave entrainment frequencies induce specific states of mind, which are the result of those brainwaves, delivering them in pleasing and relaxing audio tracts for use with and without stereo headphones. For example, alpha and theta waves, because they exist at the borders between conscious and unconscious thought, are especially rich and useful for tapping into and stimulating subconscious processes.

Similar to research into state changes in brain function, older studies make more specific claims about trait changes in meditators versus non-meditators. Changes to the alpha wave were indicated to be a trait, as well as state, phenomena. Studies have reported an increase in the specific frequencies expressed in the alpha range, increased alpha band power, and an overall slowing (reduction in frequency) in EEG activity in experienced meditators versus less experienced meditators while meditating.[5][10] The alpha blocking phenomena, observed as a state change in brain function, was investigated as a possible trait change as well. One study that examined a variety of meditation techniques tried to show that alpha blocking was affected by the long term practice of meditation by testing response to auditory stimuli.[11] Review works, however, comment on inconsistent findings as well as a lack of repeated results in this, and other studies. They further remark that, similar to observations in brain state changes, only general assertions can be made about brain trait changes: some change in the electroencephalographic profile exists but with some inconsistency.[4][12] It is also important to note that these trait changes were observed during meditation, and although it does indicate that a practitioner’s electroencephalographic profile is modified by the practice of meditation, these EEG studies have not yet shown changes in non-meditating brains, even of experienced meditators.
Brain Wave Entrainment is any procedure that causes one's brainwave frequencies to synchronize with a periodic stimulus (sound, vibration or light) having a frequency corresponding to the intended brain-state (for example, to induce a trance, dreams, sleep or relaxation.) It is also called the Flicker-response because of how staring at a campfire or the flickering of a burning candle can lull you into a state of calmness and serenity. There was an extensive article on this phenomenon by Gerard Oster in Scientific American in 1973. It may sound novel, but in many ways, this is old tech. 

But what would be the point of generating a beat that was at the same rate as a certain brainwave frequency? First, consider that these frequency bands relate to different states of awareness. Delta is seen in deep sleep, theta in lighter stages of sleep, alpha when we are relaxed with eyes closed, and beta when we are awake and alert. Second, the main idea behind using binaural beats to help a person relax and sleep is that of entrainment. Entrainment means that a biological process is matched to some external stimulus. For example, our circadian clock is entrained to the day/night light cycle and helps the body organize physiological processes in an appropriate way over the course of the day. A repetitive sound at the frequency of a certain brainwave band could theoretically cause the brain waves to be entrained to that frequency and thus help induce the state associated with that brainwave band. This could have therapeutic utility.
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.

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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.
"The brain is set up in such a way as to have spiritual experiences and religious experiences," said Andrew Newberg, a Philadelphia scientist who authored the book "Why God Won't Go Away." "Unless there is a fundamental change in the brain, religion and spirituality will be here for a very long time. The brain is predisposed to having those experiences and that is why so many people believe in God."
From a brainwave entrainment effectiveness perspective, it’s my understanding that the response from isochronic tones stimulation starts to diminish over 30Hz and that 40Hz is about the limit for using them. So from what I’ve read on the topic a 100Hz beat wouldn’t work, probably because it’s too fast for the brain to process and synchronise with it.
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.
Since opening their online store in 2011, Binaural Beats Meditation has served “hundreds of thousands” of customers, according to James Matthews, the site’s customer happiness manager. “We continue to see an increase in interest… from individuals, but increasingly so from therapists using the music to help clients, health and wellness organizations, and businesses around the world.”
A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion:
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