Reverberant Field Tail | WaitWhatAudio

Interactive Acoustic Soundstage Guide

1. Configure Dimensions

Adjust the slider inputs to modify the physical volume parameters and see the bounding walls physically scale in real-time.

2. Trigger Impulse

Click the Fire Acoustic Impulse button to excite the soundstage room with an instantaneous energy spike.

3. Analyze the Tail

Watch the chaotic sound particle cloud scatter and map its monotonic logarithmic drop-off curve on the chronograph timeline.

Statistical Decay Simulator

Modify structural volume, surface area boundaries, and materials absorption profiles to calculate real-time reverberation decay slopes ($RT_60$). Fire an impulse trigger to capture the geometric tail dissipation curve.

Room Volume (V): 150 m³

Average Absorption (α): 0.15

Acoustic Excitation

Diffuse Particle Decay Soundstage

Logarithmic Energy Attenuation Slope ($RT_60$ Chronograph)

Statistical Tail Tracking

Awaiting acoustic impulse excitation trigger...

Calculated Sabins ($A$)

Total equivalent absorption area square units

Target $RT_60$ Time

Time frame required for a -60dB energy drop-off

Tail Field Density Profile

Statistical spacing index of decaying nodes

The Core Formulation: Wallace Clement Sabine's Legacy

Reverberant tails represent the point where tracking individual reflection paths becomes physically impossible. Instead, we treat the remaining sound field as a statistical gas compressing and escaping through absorbent windows.

Acoustic Proof

The Classical Sabine Formula & Air Attenuation Exponent

The target timing parameter required for a sound field to decay exactly 60dB below its initial structural excitation energy is mapped directly via room metrics:

$$RT_{60} = \frac{0.161 \cdot V}{A} = \frac{0.161 \cdot V}{\sum S_i \alpha_i}$$

For critical spaces with exceptionally high absorption properties ($\alpha > 0.35$), the standard Sabine calculation breaks down due to logarithmic singularities. In these profiles, the architectural model pivots to the **Eyring-Norris equation framework**:

$$RT_{60} = \frac{0.161 \cdot V}{-S \cdot \ln(1 - \alpha_{\text{mean}}) + 4mV}$$

Total Sabins ($A$)

Acoustic Open Window Equivalent: Calculated by summing up every single physical plane's boundary surface area ($S$) multiplied by its custom material absorption rating ($\alpha$). One Sabin is equal to one square meter of a totally open boundary pointing out into empty space.

Air Attenuation ($4mV$)

<strong>High-Frequency Atmospheric Friction:</strong> The factor $m$ represents the energy loss per meter as sound waves pass directly through air molecules. At frequencies past $10\text{ kHz}$, air friction absorbs tail energy faster than the actual physical walls of your studio monitor tracking rooms.