Binaural beats occur when two separate carrier tones with slightly different frequencies are played in each ear.

For example, let's say you listen to a sound with a frequency of 200 Hz in the left ear and another sound with a frequency of 210 Hz in the right ear.

Your mind combines and interprets these two tones into a single sound (or "amplitude modulated standing wave") which you can "hear" in your mind only. You'll know it's a binaural beat because it has a distinctive pulsing sound, with a "wah-wah" sound or rhythm.
If you really want to be sure that you’re listening to binaural-beats, one way is to remove one of the headphones, leaving the other earphone on.

You’ll notice that the "wah-wah" sound goes away leaving behind a flat sound. Bring the earphone back and the "wah-wah" sound comes back too.
Now, remember that you actually only "perceive" the combined beats in your mind only. The human ear can only hear between 20 to 20,000 Hz, so obviously, you won’t be able to hear a tone with a frequency of only 10 Hz!
Anyway, the net result is that your brain waves will "entrain" to the frequency of the binaural beats.

This is actually one of the easiest ways of actually slowing down your brainwave patterns to achieve whatever brain wave state you want. It doesn’t matter what frequency you use, what’s more important is the frequency difference between the two tones.

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Binaural beats can easily be heard at the low frequencies (< 30 Hz) that are characteristic of the EEG spectrum (Oster, 1973). This perceptual phenomenon of binaural beating and the objective measurement of the frequency-following response (Hink, Kodera, Yamada, Kaga, & Suzuki, 1980) suggest conditions which facilitate entrainment of brain waves and altered states of consciousness.

There have been numerous anecdotal reports and a growing number of research efforts reporting changes in consciousness associated with binaural-beats. "The subjective effect of listening to binaural beats may be relaxing or stimulating, depending on the frequency of the binaural-beat stimulation" (Owens & Atwater, 1995).

Binaural beats in the delta (1 to 4 Hz) and theta (4 to 8 Hz) ranges have been associated with reports of relaxed, meditative, and creative states (Hiew, 1995), and used as an aid to falling asleep. Binaural beats in the alpha frequencies (8 to 12 Hz) have increased alpha brain waves (Foster, 1990) and binaural beats in the beta frequencies (typically 16 to 24 Hz) have been associated with reports of increased concentration or alertness (Monroe, 1985) and improved memory (Kennerly, 1994).

Passively listening to binaural beats may not spontaneously propel you into an altered state of consciousness. One’s subjective experience in response to binaural-beat stimulation may also be influenced by a number of mediating factors.

For example, the willingness and ability of the listener to relax and focus attention may contribute to binaural-beat effectiveness in inducing state changes. "Ultradian rhythms in the nervous system are characterized by periodic changes in arousal and states of consciousness (Rossi, 1986;Shannahoff-Khalsa, 1991; Webb & Dube, 1981).

These naturally occurring shifts may underlie the anecdotal reports of fluctuations in the effectiveness of binaural beats. External factors are also thought to play roles in mediating the effects of binaural beats" (Owens & Atwater, 1995). The perception of a binaural beat is, for example, said to be heightened by the addition of white noise to the carrier signal (Oster, 1973), so white noise is often used as background.

 "Music, relaxation exercises, guided imagery, and verbal suggestion have all been used to enhance the state-changing effects of the binaural beat" (Owens & Atwater, 1995). Other practices such as humming, toning, breathing exercises, autogenic training, and/or biofeedback can also be used to interrupt the homeostasis of resistant subjects
(Tart, 1975).