The Theory of Binaural Beats
George Walter Stewart · Physical Review · 1917
A S described in preceding articles on binaural beats, 1 there are several phenomena that invite an explanation in terms of physics.The three outstanding aspects are (i) the existence of the "binaural" beats, herein referred to as " primary" beats which correspond to these heard uniaurally with two forks almost in unison, (2) the distinct perception of secondary intensity-maxima when the binaural beat-period is greater than two to five seconds, and (3) the wandering localization of the sound during each beat.We will consider these three separately and propose a theory which seems to promise a satisfactory explanation. PRIMARY BEATS.Dove 2 in 1839 discovered that when two forks, almost in unison, were presented first to one ear and then, by carrying one about the head, one to each ear, the beats perceived in the first position disappeared and subsequently reappeared as the moving fork approached its final position.I have chosen to call these binaural beats the "primary" beats, for they are always present with observers who are not seriously deaf in one ear.This is not true of the "secondary" beats which occur with clearness only if the primary beat-period exceeds two to five seconds, Separate treatment of the primary beats is justifiable, and in order to make the theory conform strictly to the fact, let us suppose we are dealing with a primary beat-period of approximately one second, or a period where the primary beats alone appear.As already described, 3 we have then a maximum with o° and a minimum with 180 0 phase differences.Let us assume that the forks Fi and F2 are presented one to each ear, that their amplitudes are equal, that Fi has the greater frequency, and that there are conducting paths from each fork to the farther ear.Let ei be the retardation in phase in transmission from each fork to the nearer ear.(By the "ear" is meant the physical instrument producing the sensation.)