Beats in Dichotic Listening

(G. W. Stewart. Binaural beats. Phys. Review 9, p. 502—1917; G. W. Stewart. The secondary intensity maxima in binaural beats. Phys. Review, 9, p. 509—1917).

The fact that beats exist when sounds differing slightly in pitch are delivered separately to the two ears (dichotically) has been the subject of study by many investigators (Dove, Purkyně, S. Thompson, Rayleigh, More, Wilson, Rostosky, and others). G. Stewart carried out a series of experiments on a large number of persons, the results of which may be summarized as follows.

Beats are observed irrespective of whether the sound is heard with one ear or separately with the two. When the phase difference of separately heard sounds is \(=0\), the sound seems to the observer to come from in front; with a phase difference of about \(180^\circ\), from behind; with a phase difference of about \(90^\circ\), from the side (on the side of the source of the sound of higher frequency); and with a phase difference of about \(270^\circ\), from the other side (the source of the sound of lower frequency). During one beat the sound source seems to change its position in a circle. In intensity, the sound has, over the period of one beat, three maxima: one, the largest, at a phase difference \(=0\), and two others (secondary) at phase differences \(180^\circ \delta\) and \(180^\circ-\delta\), with \(\delta < 45^\circ\). The secondary maxima are perceptible only for a long beat period (not less than one second). The value \(\delta\), being independent of the beat period but dependent on the pitch of the tone, increases precisely with its pitch. For sounds of different pitches it increases as follows:

Stewart suggested that the existence of secondary maxima may be explained by the transmission of sound from one ear to the other through the bones of the skull.

P. Belikov.