Abstract
A human listening to monophonic sound through headphones perceives the sound to emanate from a point inside the head at the auditory centre at effectively zero range. The extent to which this is predicted by synthetic-aperture calculation performed in response to head rotation is explored. The instantaneous angle between the auditory axis and the acoustic source, lambda, for the zero inter-aural time delay imposed by headphones is 90°. The lambda hyperbolic cone simplifies to the auditory median plane, which intersects a spherical surface centred on the auditory centre, along a prime meridian lambda circle. In a two-dimensional (2-D) synthetic-aperture computation, points of intersection of all lambda circles as the head rotates constitute solutions to the directions to acoustic sources. Geometrically, lambda circles cannot intersect at a point representing the auditory centre; nevertheless, 2-D synthetic aperture images for a pure turn of the head and for a pure lateral tilt yield solutions as pairs of points on opposite sides of the head. These can reasonably be interpreted to be perceived at the sums of the position vectors of the pairs of points on the acoustic image, i.e., at the auditory centre. But, a turn of the head on which a fixed lateral tilt of the auditory axis is concomitant (as in species of owl) yields a 2-D synthetic-aperture image without solution. However, extending a 2-D synthetic aperture calculation to a three-dimensional (3-D) calculation will generate a 3-D acoustic image of the field of audition that robustly yields the expected solution.