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STANDARDS OF ACOUSTICAL ENGINEERING

Room Acoustics Console

RT60 Reverberation Times and Resonant Modes

Physical Parameters

Room Dimensions
m
m
m
Atmospheric Variables
°C
%
Source and Distance
factor
m
Surface Materials
Active Mode for 3D Visualization
Equation 1: Speed of Sound
$$c = 331.3 \sqrt{1 + \frac{T}{273.15}} + 0.6 \left(\frac{RH}{100}\right) 1.2$$
Result (c): 344.0 m/s
Equation 2: Volume & Surface Area
$$V = L \cdot W \cdot H \quad | \quad S = 2(LW + LH + WH)$$
V / S: 81.0 m³ / 117.0 m²
Equation 3: Standard Sabine (500 Hz)
$$RT60_{\text{Sabine}} = \frac{0.161 \cdot V}{S \cdot \bar{\alpha}}$$
Time: 1.25 s
Equation 4: Sabine + Air Absorption
$$RT60_{\text{Sabine+Air}} = \frac{0.161 \cdot V}{S \cdot \bar{\alpha} + 4m \cdot V}$$
With Air: 1.22 s
Equation 5: Standard Eyring (500 Hz)
$$RT60_{\text{Eyring}} = \frac{0.161 \cdot V}{-S \cdot \ln(1 - \bar{\alpha})}$$
Time: 1.15 s
Equation 6: Eyring + Air Absorption
$$RT60_{\text{Eyring+Air}} = \frac{0.161 \cdot V}{-S \cdot \ln(1 - \bar{\alpha}) + 4m \cdot V}$$
With Air: 1.12 s
Equation 7: Fitzroy Model (Directional)
$$RT60_{\text{Fitzroy}} = \frac{0.161 \cdot V}{S^2} \left[ \frac{S_x}{\bar{\alpha}_x} + \frac{S_y}{\bar{\alpha}_y} + \frac{S_z}{\bar{\alpha}_z} \right]$$
Fitzroy RT60 (500 Hz): 1.35 s
Equation 8: Arau-Puchades Model (Directional Exponential)
$$RT60_{\text{Arau}} = \prod_{i=x,y,z} \left(\frac{0.161 \cdot V}{-S \cdot \ln(1 - \bar{\alpha}_i)}\right)^{\frac{S_i}{S}}$$
Arau RT60 (500 Hz): 1.28 s
Chart 1: RT60 Octave Band Comparison Comparison of Stochastic and Directional Models (125 Hz - 4 kHz)
Chart 5: Material Absorption Coefficients Absorption curves of selected materials
Chart 10: Equivalent Absorption Area (Sabines) Distribution by frequency bands
Equation 9: Normal Frequencies (3D Modes)
$$f_{p,q,r} = \frac{c}{2} \sqrt{\left(\frac{p}{L}\right)^2 + \left(\frac{q}{W}\right)^2 + \left(\frac{r}{H}\right)^2}$$
Selected Mode $f_{1,0,0}$: 28.7 Hz
Equation 10: Schroeder Frequency (Modal Limit)
$$f_s = 2000 \sqrt{\frac{RT60_{500}}{V}}$$
Transition Frequency ($f_s$): 248.3 Hz
Chart 2: Modal Frequency Spectrum (20 - 250 Hz) Red=Axial, Green=Tangential, Purple=Oblique. Click to select mode.
Chart 3: Modal Density (Bonello Criterion) 1/3 Octave Count. Orange/Red indicates density drop (poor distribution).
Chart 4: Bolt Ratio Diagram L/H vs W/H ratios. Cyan region = optimal modal distribution.
Chart 11: 3D Acoustic Pressure Fields (WebGL) Antinodes (Red/Orange) vs Nodes (Cyan/Blue). Drag to rotate.
First 15 Normal Modes Ordered by Frequency
Mode (p, q, r) Frequency (Hz) Type Period (ms) Wavelength (m)
Equation 11: Critical Distance ($D_c$)
$$D_c = 0.141 \sqrt{Q \cdot S \cdot \bar{\alpha}_{500}}$$
Critical Distance ($D_c$): 1.84 m
Equation 12: Average Absorption Coefficient ($\bar{\alpha}$)
$$\bar{\alpha} = \frac{\sum_{i} S_i \alpha_i}{S}$$
Weighted (500 Hz): 0.18 α
Chart 6: SPL vs Distance (Direct vs Diffuse) Source decay and Critical Distance point (total field)
Chart 7: Schroeder Frequency vs RT60 Modal limit evolution across reverberation time sweep
Chart 8: 2D Early Reflections Simulator 1st Order Reflections. Drag Source (S) or Receiver (L)
💡 Drag point S or L with the cursor to calculate reflections.

Flight Times and Delay

Chart 9: Modal Decay Waterfall Room resonance spectrum in 50ms intervals

Spectral Decay Physics

Each curve represents the modal decay at a time $t$. The peaks correspond to the calculated normal modes. The attenuation of each mode depends on the absorption of the materials in its band and its damping $e^{-6.91 t / RT60}$.