Bill Hartmann's influence on computational psychoacoustics: Extending and correcting the Woodworth model

Bill Hartmann’s approach to acoustics through the lens of physics led to novel advancements in acoustical models relevant especially to psychoacoustical applications. While the method of computing interaural time and level differences using an exact diffraction model of a rigid, spherical head is well established, utilizing it in cases where high precision is required, especially at high frequencies, is computationally taxing. The Woodworth formula computes the interaural time difference for a rigid, spherical head, assuming plane-wave incidence (i.e. large source distance) and antipodal ears, based on a computationally efficient ray-tracing acoustical model with a creeping-wave solution. It is only applicable as a high-frequency limit (wavelength much smaller than the head radius), viable for adult human heads above approximately 4 kHz. It further assumes that there is only one creeping-wave path around the head—that of shortest distance—even when paths around the front and back of the head are almost the same length. This approximation is compared to an exact rigid spherical head model, extended to allow for arbitrary ear locations and non-distant sources, and corrected to include both creeping waves while maintaining low computational complexity [Aaronson and Hartmann, J. Acoust. Soc. Am. 135, 817–823 (2013)].