The Function of Intensity and Phase in the Binaural Location of Pure Tones. II

Abstract

Linear Relation; Phase Difference and Apparent Angular Displacement of the Source of Sound.---That a linear relation exists between phase difference at the ears and apparent angular displacement from the median plane between them, is demonstrated for pure tones within the range 100 to 1,200 d.v. Extended experiments are made with two individuals but additional evidence is adduced to show that the results have a general applicability.Linear Relation; the Variation of the Constant with Frequency.---The constant in the above linear relation, or the slope of the curve with the two variables as coordinates, is approximately a linear function of the frequency.Upper Limit of the Phase Difference Effect.---The upper limit of the phase difference effect seems to be from 1,000 to 1,500 d.v.Double Images.---It is shown that the phase difference effect, if it be the controlling factor in localization, may produce multiple apparent sources. For a frequency of 1,024 d.v., the double phantom sources are found in actual experiment to have the relative positions indicated by the phase effect.Intensity-effect and Phase-effect Combined.---It is found that when intensity difference and phase difference at the ears exist simultaneously, neither has a greater effect than when applied separately. Hence quantitative results obtained by using intensity difference only or phase difference only are transferable to the case of the combination.Direct Perception of Phase.---Phase effect cannot be explained by a direct or by an indirect effect of intensity, for the phase effect at certain frequencies and with some individuals may exist when the intensity effect is wholly absent. Direct perception of phase is thus evident.Theoretical Computation and Comparison with Experiment.---The phase difference at the ears for various angular displacements of the source from the median plane are computed for three frequencies scattered over the range under consideration. The relationship is not strictly linear but very roughly so. A comparison is made of the theoretical and experimental ratios of angular displacement and phase difference. There is a satisfactory quantitative agreement.Phase Difference the Most Important Factor in Localization.---The significance of the quantitative agreement of experimental and theoretical results is presented and the conclusion derived that phase difference is the most important factor in localization of the source of a pure tone, 100 to 1,200 d.v. situated in a horizontal plane in front of the observer and 90\ifmmode^\circ\else\textdegree\fi{} either side of the median plane. This conclusion is extended to include the region behind as well as in front of the observer. There are more factors in actual localization than in the case assumed in the theoretical discussion; for example, reflection and alterations in quality are doubtless important factors in the general case. Above the limit of the phase difference phenomenon, viz., approximately 1,200 d.v., intensity must become an important factor, but its importance varies with the individual.