Interaural time delay calculations must account for sound traveling around the head

Evidence

Unfortunately, this equation is wrong. It underestimates the delay between the ears because it ignores the fact that the sound must travel around the head in order to get to them. This adds an additional delay to the sound, as shown in Figure 2.25. This additional delay can be calculated, provided one assumes that the head is spherical, by recognizing that the distance traveled around the head for a given angle of incidence is given by: where ∆d = the extra path around the head at a given angle of incidence (in m) and r = half the distance between the ears (in m) This equation can be used in conjunction with the extra path length due to the angle of incidence, which is now a function of r, as shown in Figure 2. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 710

This equation can be used in conjunction with the extra path length due to the angle of incidence, which is now a function of r, as shown in Figure 2.25, to give a more accurate equation for the ITD as: FIGURE 2. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 713

Unfortunately this equation is wrong. It underestimates the delay between the ears because it ignores the fact that the sound must travel around the head in order to get to them. This adds an additional delay to the sound, as shown in Figure 2.23. This additional delay can be calculated, provided one assumes that the head is spherical, by recognizing that the distance traveled around the head for a given angle of incidence is given by: where the extra path round the head at a given angle of ∆d  incidence in m and half the distance between the ears This equation can be used in conjunction with the extra path length due to the angle of incidence, which is now a function of r, as shown in Figure 2. — David Howard, Jamie Angus, coustics and Psychoacoustics, 705

Categorization

• QUESTION: A real head is not spherical — worth noting whether the spherical-head assumption introduces meaningful error in practice, and how more realistic models improve the ITD estimate.
• DEFINE: Shows how the head-related extra path — angle-dependent radius term — folds into the ITD formula.
• XREF: A naive line-of-sight distance model fails; the correct model treats the head as a diffracting sphere — echoes the theme elsewhere in the chapter that simple geometric models understate acoustic reality. — connects to: Directional hearing rests on interaural time and intensity differences. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 704
• corroborated: 3 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 710; David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 713; David Howard, Jamie Angus, coustics and Psychoacoustics, 705