# Ten Microseconds Between the Ears: The Biophysics of Sound Localization

When a sound originates from one side, the acoustic wave reaches one ear a fraction of a millisecond before the other. The human brainstem detects arrival disparities as small as 10 microseconds — an interval 100 times shorter than the duration of a single action potential (1.0 ms), corresponding to an acoustic path in air of just 3.4 millimetres.

## Key Indicators

- **Minimum Detection Threshold (ITD):** 10 µs (at the head midline, 0° azimuth).
- **Maximum Delay at 90°:** ~656 µs (for a 17.5 cm head diameter at a speed of sound of 343 m/s).
- **Neural Temporal Ratio:** 100 : 1 (an action potential lasts 1,000 µs, while the medial superior olive resolves 10 µs arrival offsets).
- **Physical Acoustic Path at Threshold:** 3.43 mm (at 343 m/s speed of sound).
- **Minimum Audible Angle (MAA):** 1.0°–2.0° on the frontal midline.

## 1. Psychoacoustic Test & Pure Temporal Delay

At low frequencies (below 1,500 Hz), sound waves diffract around the human head without creating significant volume shadows. The brain determines source direction purely through phase differences and arrival timing at the two eardrums.

- An ITD of -656 µs localizes the sound fully to the left ear (90° left).
- An ITD of -261 µs corresponds to an azimuth of 30° left.
- An ITD of 0 µs places the sound directly at the intracranial center.
- An ITD of +261 µs corresponds to an azimuth of 30° right.
- An ITD of +656 µs localizes the sound fully to the right ear (90° right).

## 2. The Jeffress Neural Circuit Model (MSO)

Formulated by Lloyd Jeffress in 1948, the model explains how the auditory brainstem converts time differences into a spatial topographic map:
- Axons from the anteroventral cochlear nucleus (AVCN) on both sides function as calibrated biological delay lines.
- Bipolar neurons in the medial superior olive (MSO) serve as coincidence detectors.
- A given MSO neuron discharges an action potential only when input pulses from both ears arrive synchronously at its soma.
- Low-voltage-activated potassium channels (*K_v1.1*) and giant Endbulbs of Held shorten excitatory postsynaptic potentials (EPSPs) to under 0.2 ms, eliminating temporal jitter.

## 3. The Woodworth Spherical Model

The mathematical relationship between sound incidence angle *θ* (in radians) and Interaural Time Difference (ITD) is given by the Woodworth-Schlosberg equation:
`ITD = (r / c) * (θ + sin θ)`

where:
- `r` is the equivalent head radius (~8.75 cm for a 17.5 cm bitragus distance);
- `c` is the speed of sound in air (343 m/s at 20°C);
- `θ` is the sound azimuth angle in radians.

Underwater, the speed of sound rises to approximately 1,480 m/s (4.3 times faster than in air). The maximum interaural delay collapses to under 160 µs, while skull bone conduction bypasses middle ear isolation, eliminating directional hearing in submerged humans.

## 4. Four Stages of Binaural Processing

1. **Inner Ear (Organ of Corti):** Phase locking of receptor potentials to the acoustic wave cycle below 1,500 Hz.
2. **Cochlear Nucleus (Endbulbs of Held):** Giant synapses with ultrafast AMPA receptor kinetics (< 0.2 ms).
3. **Medial Superior Olive (MSO):** Jeffress delay lines and coincidence detection for ITD (10–20 µs resolution).
4. **Lateral Superior Olive (LSO):** Interaural Level Difference (ILD) processing for high frequencies (> 3,000 Hz) via cross-glycinergic inhibition.

## Scientific References

- Jeffress, L. A. (1948). *A place theory of sound localization*. Journal of Comparative and Physiological Psychology, 41(1), 35–39.
- Rayleigh, Lord (1907). *On our perception of sound direction*. Philosophical Magazine, 13(74), 214–232.
- Woodworth, R. S., & Schlosberg, H. (1954). *Experimental Psychology*. Holt, Rinehart and Winston, New York.
- Yin, T. C., & Chan, J. C. (1990). *Interaural time sensitivity in medial superior olive of cat*. Journal of Neurophysiology, 64(2), 465–488.
- Grothe, B., Pecka, M., & McAlpine, D. (2010). *Mechanisms of sound localization in mammals*. Physiological Reviews, 90(3), 983–1012.