Binaural localisation simulator — spherical head model

Drag the blue source or use the sliders. Values update in real time. This model uses the Woodworth spherical head ITD approximation and a frequency-dependent head-shadow approximation for ILD (dB).
ITD: 0.00 ms
ILD: 0.00 dB
Angle: 0°
Distance: 1.0 m
Freq: 1000 Hz
Model notes: Ear positions are ±headRadius on the x-axis. ITD uses the Woodworth spherical head formula. ILD uses inverse-distance law for pressure plus a simple frequency-dependent head-shadow attenuation (max attenuation between 200 Hz and 8000 Hz).
30°
1.00 m
1000 Hz
Drag source in the SVG with the pointer.

Explanation

This interactive demo uses a simple spherical head model:
  • Interaural Time Difference (ITD): Woodworth spherical head approximation, head radius r = 0.0875 m, sound speed c = 343 m/s:
    \[ \text{ITD}(\theta) = \begin{cases} \frac{r}{c} (\sin \theta + \theta), & |\theta| \le 90^\circ \\[2mm] \frac{r}{c} (\sin \theta + \pi - \theta), & |\theta| > 90^\circ \end{cases} \]
  • Interaural Level Difference (ILD): Amplitude scales as 1/distance. ILD (dB) = 20·log10(P_left / P_right). Extra attenuation is applied to the contralateral ear depending on frequency (200–8000 Hz).
  • Azimuth convention: θ = 0° in front, +90° to the right ear.