Module 3: Spatial Fields

Early Reflections (The Boundary Bounce)

Visualizing real-time specular boundary tracking. Observe how acoustic wave vectors reflecting from physical walls create a time-delayed ghost duplicate that corrupts the transient coherence of direct audio.

Ray-Tracing Boundary Engine

Simulate specular room reflections. Adjust the room width parameters and listener offset positioning to map structural time-of-arrival delays and calculate active comb filtering null profiles.

Live Soundstage Vector Map
Impulse Response (IR) Timeline Window (Time of Arrival Relative to Direct Signal)
Direct-to-Reflection Δt
--
Initial arrival lag interval time scale
Interaural Cross-Correlation (IACC)
--
Estimated spatial coherence trend profile
Comb Filtering Threat Level
--
Phase cancellation severity assessment

The Layman Breakdown: The Direct Punch vs. Room Smear

When an acoustic monitor cone generates energy, the physical air particles radiate a spherical pressure sphere. What follows is a temporal race against architectural geometry.


The Direct Punch Path

The pure wavefront traveling unhindered along the absolute shortest vector directly into your ears. This line dictates clean transient definition, crisp imaging localization, and real phase timing.

Because this ray traverses the least physical space, it serves as the master phase time reference point for your primary auditory positioning mechanics.

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The Boundary Room Smear

The secondary vector duplicates which strike the side boundaries, floor, or ceiling before bouncing backward. Because they fly a longer path, they arrive a few milliseconds behind the master stream.

Your brain integrates arrivals within a 30 ms window together. Instead of an echo, you perceive it as tonal distortion, local blurriness, and phase-scooped response traps.

Acoustic Proof

Boundary Vector Geometry & Comb-Filtering Subtraction Physics

Speculated reflections can be perfectly calculated by creating virtual coordinate points mirrored past boundary barriers. Applying the Pythagorean theorem provides exact path distances:

$$d_{\text{reflect}} = \sqrt{x^2 + y^2}$$

This extra path tracking distance delays the reflection vector relative to the direct line. The delay timeline gap causes continuous cycles of phase-destructive interference. The fundamental cancellation frequency null is localized via:

$$f_{\text{null}} = \frac{1}{2 \cdot \Delta t} \quad \text{where} \quad \Delta t = \frac{d_{\text{reflect}} - d_{\text{direct}}}{c}$$
Speed ($c$)
Speed of Sound Vector: Standardized at $c \approx 343\text{ m/s}$ under common atmospheric criteria. This constant determines how quickly spatial gaps convert into temporal comb frequencies.
Delta Time ($\Delta t$)
The Destructive Window: The critical interval time gap between arrivals. When this gap narrows, the fundamental acoustic null points shift straight upward into critical mid-range spectrum targets.