There are many advantages and disadvantages with binaural beats. One of the major advantages is hemispheric synchronization. Since both hemispheres are required to create the beat within the brain, this method is an excellent way to create greater harmony between areas of the mind typically functioning independently. Binaural beats are also known to have effective hypnotic and relaxing effects.
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.
Alpha is the next level down, between 8Hz - 12Hz, corresponding to being awake but deeply relaxed. It can be a little confusing that Alpha is lower than Beta, but it is named that way because Alpha was the first brainwave "discovered" (identified) by Hans Berger in 1929. Meditating in this state is very relaxing and most people find it very easy to become entrained in this frequency.

Recently developed entrainment software has been designed to correct specific imbalances in hemispheric activity associated with undesirable mind-states. For example, people suffering with depression often have more activity in the right hemisphere, and specially designed brainwave music decreases this activity while increasing activity in the left hemisphere, reducing depression.

Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
Basically, "two ears." One usage of the word is "binaural recording," which is a form of stereo recording meant to take advantage of the spatial perception of the human ear. Recordings are usually done using a pair of microphones mounted to a dummy head with roughly accurate models of the human outer ear, and the result when played back through headphones is extremely realistic and comparable to surround sound, though following an entirely different recording model. Binaural recordings aren't woo at all, and have nothing to do with binaural beats.[citation needed]
Delta brain state is related to the unconscious or super-conscious mind. Delta waves are the slowest of all five brainwave frequencies. These brain waves are generated in deep sleep and in very deep meditation. In the sleep cycle, the deepest of sleep states is called “Slow Wave Sleep” (SWS). In this phase, the brain begins producing very slow, large Delta waves. The deeper the sleep, the higher the amount of delta waves. This stage plays a vital role in health and well-being, especially because healing and regeneration processes are stimulated in this state. In the Delta state, you do not dream, you are completely unconscious.
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.

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Hi Ulka, thanks for your compliment on my article. Unfortunately, I haven’t come across any studies or much discussion about the problem with habituation and isochronic tones and how to overcome it. The consensus among experienced users is to regularly change the frequencies and music soundtracks you listen to. Adding music to the tones does change the waveform you are stimulated with, so that’s one of the main reasons why I provide different soundtracks for my isochronic tones sessions. I have released some tracks which use amplitude modulations in the music, instead of isochronic tones. It might be worth giving them a try if you haven’t already. I have them in a playlist on YouTube
The various mental states of the individual are thought to take place across a varied range of frequencies, or brainwaves. By encouraging the frequency following process, entrainment is able to create positive change in the brain, through matching carefully-selected frequencies of light and/or sound. The stimulus enables the individual to access a different state of consciousness, which can be useful for a number of benefits including relaxation, anxiety management, stress reduction and more.

When the track is over you can continue to meditate without the help of the entrainment track.  When you are ready to get up, thank your Higher Self for the experience and remove your blindfold, keeping your eyes closed.  Stay seated with your eyes closed for a few moments, then slowly open them and take a moment to let your eyes adjust to your environment’s light. 
It sounds like your brain might have initial trouble adapting to the binaural beats. The same thing happened to me when I listen to the Beta frequency (I got a headache), but then I discovered that I had the volume turned up too loud. I would say experiment with these frequencies, but at a low volume. See how you go. And if you continue to have anxiety, by all means, stop listening. Also, not all binaural beats are created equally. Some are amateurish, but the ones from Binaural Beats Meditation (mentioned and linked to in this article), are professionally created and the ones that I personally listen to. I love them (especially the Theta/Delta ones)! I hope this helps. :)
^ Bittman, B. B., Snyder, C., Bruhn, K. T., Liebfreid, F., Stevens, C. K., Westengard, J., and Umbach, P. O., Recreational music-making: An integrative group intervention for reducing burnout and improving mood states in first year associate degree nursing students: Insights and economic impact" International Journal of Nursing Education Scholarship, Vol. 1, Article 12, 2004.