In addition to lowering the brain frequency to relax the listener (or to raise it to help focusing), there are other controversial, alleged uses for binaural beats. For example, that by using specific frequencies an individual can stimulate certain glands to produce desired hormones. Beta-endorphin has been modulated in studies using alpha-theta brain wave training, and dopamine with binaural beats. Among other alleged uses, there are reducing learning time and sleeping needs (theta waves are thought to improve learning, since children, who have stronger theta waves, and remain in this state for a longer period of time than adults, usually learn faster than adults; and some people find that half an hour in the theta state can reduce sleeping needs up to four hours; however, this is supposed to happen with any way to get into theta state, e.g. meditation;) some use them for lucid dreaming and even for attempting out-of-body experiences, astral projection, telepathy and psychokinesis. However, the role of alpha-wave activity in lucid dreaming is subject to ongoing research.
Alpha-theta brainwave training has also been used successfully for the treatment of addictions, for the recovery of repressed memories, but as with other techniques this can lead to false memories.
A trial of Delta binaural beat technology over 60 days has shown positive effect on self-reported psychologic measures, especially anxiety. There was significant decrease in trait anxiety, an increase in quality of life, and a decrease in insulin-like growth factor-1 and dopamine and has been successfully shown to decrease mild anxiety and lessen hospital acute pre-operative anxiety.
Another claimed effect for sound induced brain synchronization is enhanced learning ability. It was proposed in the 1970s that induced alpha brain waves enabled students to assimilate more information with greater long term retention. In more recent times has come more understanding of the role of theta brain waves in behavioural learning The presence of theta patterns in the brain has been associated with increased receptivity for learning and decreased filtering by the left hemisphere. Based on the association between theta activity (4–7 Hz) and working memory performance, biofeedback training suggests that normal healthy individuals can learn to increase a specific component of their EEG activity, and that such enhanced activity may facilitate a working memory task and to a lesser extent focused attention.

Frequency range
> 40 Hz Gamma waves -->Higher mental activity, including perception, problem solving, fear, and consciousness

13–40 Hz Beta waves -->Active, busy or anxious thinking and active concentration, arousal, cognition

7–13 Hz Alpha waves -->Relaxation (while awake), pre-sleep and pre-wake drowsiness

4–7 Hz Theta waves -->Dreams, deep meditation, REM sleep

< 4 Hz Delta waves -->Deep dreamless sleep, loss of body awareness

(The precise boundaries between ranges vary among definitions, and there is no universally accepted standard.)
The dominant frequency determines your current state. For example, if in someone's brain alpha waves are dominating, they are in the alpha state (this happens when one is relaxed but awake). However, also other frequencies will be present, albeit with smaller amplitudes.
The brain entraining is more effective if the entraining frequency is close to the user's starting dominant frequency. Therefore, it is suggested to start with a frequency near to one's current dominant frequency (likely to be about 20 Hz or less for a waking person), and then slowly decreasing it towards the desired frequency.
Some people find pure sine waves unpleasant, so a pink noise or another background (e.g. natural sounds such as river noises) can also be mixed with them. In addition to that, as long as the beat is audible, increasing the volume should not necessarily improve the effectiveness, therefore using a low volume is usually suggested. One theory is to reduce the volume so low that the beating should not even be clearly audible, but this does not seem to be the case (see the next paragraph).

Binaural beats may influence functions of the brain besides those related to hearing. This phenomenon is called frequency following response. The concept is that if one receives a stimulus with a frequency in the range of brain waves, the predominant brain wave frequency is said to be likely to move towards the frequency of the stimulus (a process called entrainment). In addition, binaural beats have been credibly documented to relate to both spatial perception & stereo auditory recognition, and, according to the frequency following response, activation of various sites in the brain.
The stimulus does not have to be aural; it can also be visual or a combination of aural and visual. (One such example would be Dreamachine.) However, using alpha frequencies with such stimuli can trigger photosensitive epilepsy.
Perceived human hearing is limited to the range of frequencies from 20 Hz to 20,000 Hz, though Infrasound - sound below 20Hz - still have scientifically observable effects on humans, however, it is not readily audible, especially at low volume levels. While the frequencies of human brain waves are below about 40 Hz. To account for this lack of perception, binaural beat frequencies are used. Beat frequencies of 40 Hz have been produced in the brain with binaural sound and measured experimentally.
When the perceived beat frequency corresponds to the delta, theta, alpha, beta, or gamma range of brainwave frequencies, the brainwaves entrain to or move towards the beat frequency. For example, if a 315 Hz sine wave is played into the right ear and a 325 Hz one into the left ear, the brain is entrained towards the beat frequency (10 Hz, in the alpha range. Since alpha range is associated with relaxation, this has a relaxing effect or if in the beta range, more alertness. An experiment with binaural sound stimulation using beat frequencies in the Beta range on some participants and Delta/Theta range in other participants, found better vigilance performance and mood in those on the awake alert state of Beta range stimulation.
Binaural beat stimulation has been used fairly extensively to induce a variety of states of consciousness, and there has been some work done in regards to the effects of these stimuli on relaxation, focus, attention, and states of consciousness. Studies have shown that with repeated training to close frequency sounds that a plastic reorganization of the brain occurs for the trained frequencies and is capable of asymmetric hemispheric balancing.