Binaural Beats Explained

Binaural Beats or binaural tones are auditory processing artifacts, that is apparent sounds, the perception of which arises in the brain independent of physical stimuli. This effect was discovered in 1839 by Heinrich Wilhelm Dove.
In nature, two sounds that are similar but slightly shifted in frequency will beat to produce two new frequencies which are the sum and the difference of the original two sounds. For example, a 400 Hz tone and a 410 Hz tone will form a ~405 Hz tone pulsating 10 times per second.

The brain produces a similar phenomenon internally, resulting in low-frequency pulsations in the loudness of a perceived sound when two tones at slightly different frequencies are presented separately, one to each of a subject's ears, using stereo headphones. A beating tone will be perceived, as if the two tones mixed naturally, out of the brain. The frequency of the tones must be below about 1,000 to 1,500 hertz for the beating to be heard. The difference between the two frequencies must be small (below about 30 Hz) for the effect to occur; otherwise the two tones will be heard separately and no beat will be perceived.

http://prola.aps.org/abstract/PR/v26/i3/p401_1

By introducing a tone of frequency f into one ear and another tone of frequency f+N into the opposite ear, where N is less than 5 or 6 cycles, two kinds of binaural beats are obtained. Objective binaural beats are heard for most values of f within the audible frequency range, provided there is the proper difference in amplitude between the two tones. For telephone receivers as sound sources, this difference for best beats is about 55 TU and for the same receivers supplied with sponge-rubber cushions about 62 TU. These beats are heard because the louder tone is conducted through the head to the ear of the weaker tone and the two tones there are about equally loud. Subjective binaural beats are heard for frequencies below 800 or 1000 cycles when the tones at the two ears have about the same amplitudes, differing by not more than 25 TU. Data obtained with 22 observers are summarized. The evidence indicates that these beats are not due to cross conduction but are of central origin and the result of the sense of binaural localization of sound by phase. If the beats are slow (less than 1 per sec.) they are generally recognized as an alternate right and left localization, though some observers may report one or more intensity maxima during the beat cycle. Such maxima are explained as the result of one's interpreting the sound as louder when localization is more definite. Fast beats (more than 1 per sec.) are generally recognized as an intensity fluctuation. They are explained by assuming that the sound appears louder when the phase relations are such that it is normally best localized in the position toward which the attention is directed. This explanation is supported by observations made with a constant source rotating around the head of a listener.