Module 3: Spatial Fields & Environments

Near Field vs. Far Field

The invisible boundary where chaotic audio pressure zones transform into smooth, predictable wavefronts. Learn how large loudspeaker arrays warp local phase interaction before traditional air drop-off math takes over.

Acoustic Field Propagation Engine

Simulate localized wave vectors radiating from a multi-driver loudspeaker chassis. Adjust driver array sizing and frequency parameters to watch the chaotic hydrodynamic near-field boundary morph into a uniform far-field plane wave.

Acoustic Vector Soundstage
Sound Pressure Level (SPL) Decay Profile (Inverse-Square Law Tracking)
Current Auditory State
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Active localized pressure envelope
Rayleigh Distance Boundary (R_c)
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Calculated transition threshold cross point
SPL Math Predictability
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Logarithmic geometric field stability status

The Layman Breakdown: Chaotic Proximity vs. Uniform Space

Standing right up against a massive concert line-array sounds completely different than listening from fifty rows back. This isn't just about volume; you are crossing an unmapped physical threshold.


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The Hydrodynamic Near Field

When you are closer to a multi-driver speaker than the width of the cabinet itself, your ears pick up independent sound vectors from each individual component. The high-frequency tweeter, the midrange cones, and the low-frequency woofers hit you from slightly different physical layout angles.

In this zone, moving your head a mere two inches can completely alter the frequency response. The vectors violently add and cancel each other out, making all acoustic measurement math useless.

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The Geometric Far Field

Once you travel past the critical crossover boundary, those independent acoustic vectors have traveled far enough to merge completely into a single, perfectly unified spherical wavefront. The speaker array begins acting as a singular point source.

In the far field, phase interactions stabilize. The volume decreases consistently at a predictable drop-off rate of exactly 6dB with every doubling of physical distance.

Acoustic Proof

Rayleigh Distance Equations & Phase Convergence Criteria

The mathematical boundary dividing fields—known as the Rayleigh Distance ($R_c$)—depends entirely on the relationship between the physical size of the emitting array ($D$) and the wavelength ($\lambda$) of the frequency being pushed:

$$R_c \approx \frac{2 D^2}{\lambda} = \frac{2 D^2 f}{c}$$

Inside this boundary ($R < R_c$), phase variations create sharp pressure shifts because the distance difference between your ear and the edge of the driver changes drastically. Outside ($R \ge R_c$), path length discrepancies approach zero, stabilizing the inverse relationship of acoustic pressure:

$$p(r) \propto \frac{1}{r} \quad \text{and} \quad L_p = L_{w} - 20\log_{10}(r) - 11$$
Array Size ($D$)
Acoustic Aperture: The total structural height or width of the driver system. Doubling the size of your speaker cabinet increases the chaotic near-field zone by a factor of four.
Wavelength ($\lambda$)
Frequency Scaling: High treble tones have short wavelengths, forcing their chaotic near fields further out into the room. Low bass notes have massive wavelengths, making their far fields start almost immediately at the driver surface.