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.
If you search the Internet for "binaural beats" you'll quickly find there's a whole industry built on the idea that listening to binaural beats can produce all kinds of desired effects in your brain. It can alter your mood, help you follow a diet or stop smoking, get you pumped up for a competition, calm you down, put you to sleep, enhance your memory, act as an aphrodisiac, cure headaches, and even balance your chakra. Binaural-Beats.com offers a $30 CD that they call the world's first "digital drug". They claim it can get you drunk without the side effects. I-Doser.com offers a range of music tracks that they say simulates a variety of actual pharmaceuticals, such as Demerol, Oxycontin, and Vicodin. Suffice it to say that no matter what superpower you're looking for, someone on the Internet sells a binaural beat audio file claimed to provide it.
One RCT (n=108) showed significant reduction in anxiety from a single session of alpha/delta therapy for day surgery patients. A crossover RCT of a single session of theta stimulation in four healthy adults reported significant improvement from the intervention in one of five measures. Five pre/post studies reported significant benefit from the intervention for 16 of 27 outcomes.
EquiSync’s design is based on the 100’s of studies performed on the effectiveness of brainwave entrainment technology, and 1000’s of studies on the powerful benefits of meditation. If you are interested in better understanding the power of this technology and rapidly expanding field of research, then here is a very abbreviated bibliography, a very small sample of the studies out there:
This research investigates the brainwave entrainment process and aims to demonstrate the usefulness of such an approach within the framework of cognitive performance improvements. In the introductory part the theories regarding the neurophysiological structure and the psychological processing of the cognitive system are discussed, for each of their components that are considered to be relevant for this research. The hypothesis states that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition. The research variables are the cognitive performance (the dependent variable) and the brainwave entrainment (the independent variable). The brainwave entrainment program consists in the synchronized application of Alpha binaural beats and stroboscopic light, at a 10.2 Hz frequency, in a 30 minutes long session. The difference was made by the stroop effect based exercise that was used as a frame. There were 60 participants, divided into two independent samples. The two independent samples t test for the means differences was used in the statistical analysis. The obtained results by evaluations and by statistics confirmed this research's hypothesis, stating that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition.
In Theta, you are in a waking dream, receptivity is heightened and you are able to access knowledge and information that normally lies beyond your conscious awareness. As flashes of vivid imagery dance before your mind's eye, you may feel a "floating" sensation as your mind expands beyond the boundaries of your body. In this deeply relaxed state don't be surprised to receive sudden insights, inspiration or a sense of knowing.

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.
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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.

Resonant entrainment of oscillating systems is a well-understood principle within the physical sciences. If a tuning fork designed to produce a frequency of 440 Hz is struck (causing it to oscillate) and then brought into the vicinity of another 440 Hz tuning fork, the second tuning fork will begin to oscillate. The first tuning fork is said to have entrained the second or caused it to resonate. The physics of entrainment apply to bio-systems as well. Of interest here are the electromagnetic brain waves. The electrochemical activity of the brain results in the production of electromagnetic wave forms which can be objectively measured with sensitive equipment. Brain waves change frequencies based on neural activity within the brain. Because neural activity is electrochemical, brain function can be modified through the introduction of specific chemicals (drugs), by altering the brain's electromagnetic environment through induction, or through resonant entrainment techniques.
Theta brainwaves occur most often in sleep but are also dominant in deep meditation. Theta is our gateway to learning, memory, and intuition. In theta, our senses are withdrawn from the external world and focused on signals originating from within. It is that twilight state which we normally only experience fleetingly as we wake or drift off to sleep. In theta we are in a dream; vivid imagery, intuition and information beyond our normal conscious awareness. It’s where we hold our ‘stuff’, our fears, troubled history, and nightmares.
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 auditory brainstem responses which originate in the superior olivary nucleus of each hemisphere. They result from the interaction of two different auditory impulses, originating in opposite ears, below 1000 Hz and which differ in frequency between one and 30 Hz (Oster, 1973).For example, if a pure tone of 400 Hz is presented to the right ear and a pure tone of 410 Hz is presented simultaneously to the left ear, an amplitude modulated standing wave of 10 Hz, the difference between the two tones, is experienced as the two wave forms mesh in and out of phase within the superior olivary nuclei. This binaural beat is not heard in the ordinary sense of the word (the human range of hearing is from 20-20,000 Hz). It is perceived as an auditory beat and theoretically can be used to entrain specific neural rhythms through the frequency-following response (FFR)--the tendency for cortical potentials to entrain to or resonate at the frequency of an external stimulus. Thus, it is theoretically possible to utilize a specific binaural-beat frequency as a consciousness management technique to entrain a specific cortical rhythm.  
Binaural beats are created when two tones are played simultaneously, one in each ear. As long as the difference between the two frequencies is less than 30 hertz, the brain perceives the difference in the tones as a “beat” which, if listened to with enough focus, the brain will begin to follow (this is known as the “frequency following response”). By changing the difference between the two beats, the brain will change its wavelength and enter into different “states” of being.
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. 
In physics, entrainment is the process of two oscillating systems coming to assume the same periodic rhythm, such as is observed when two clocks slowly synchronize their ticking and tick together in harmony after some time. Pendulums also achieve this same synchronicity when swinging in close proximity to one another, a phenomenon first observed and written about in 1665 by Christiaan Huygens, a Dutch scientist.
Brainwave Power Music dedicates ourselves to creating original sound therapy music, using unique Musical Compositions, Binaural Beats and Isochronic Tones as our primary sound elements mixed with different instruments and soundscapes to create a relaxed audio environment. We have one main goal: To help others through our music, be it for physical, emotional, mental or spiritual purposes. We constantly upload new music, and continue to work hard to provide new quality music for everyone.

One larger and more recent randomized and controlled trial looked at the use of binaural beats in 291 patients admitted to the emergency department at a hospital. The researchers observed significant decreases in anxiety levels in patients exposed to audio with embedded binaural beats compared to those who listened to audio without binaural beats or no audio at all (headphones only).
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. 
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.
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