Testing, correcting, and extending the Woodworth model for interaural time difference

The Woodworth model and formula for interaural time difference is frequently used as a standard in physiological and psychoacoustical studies of binaural hearing for humans and other animals. It is a frequency-independent, ray-tracing model of a rigid spherical head that is expected to agree with the high-frequency limit of an exact diffraction model. The predictions by the Woodworth model for antipodal ears and for incident plane waves are here compared with the predictions of the exact model as a function of frequency to quantify the discrepancy when the frequency is not high. In a second calculation, the Woodworth model is extended to arbitrary ear angles, both for plane-wave incidence and for finite point-source distance. The extended Woodworth model leads to different formulas in six different regions defined by ear angle and source distance. It is noted that the characteristic cusp in Woodworth's well-known function comes from ignoring the longer of the two paths around the head in circumstances when the longer path is actually important. This error can be readily corrected.