RACK/ROOMS & COVERAGE
T60T_{60}

RT60 & Critical Distance

Sabine/Eyring decay times, critical distance and speech intelligibility.

MOD-09•ARCHITECTURAL ACOUSTICS & SPEECH INTELLIGIBILITY BENCH

Reverberation Time (Sabine / Eyring RT60) & Critical Distance

Compute RT60RT_{60} decay times using Sabine and Eyring equations, determine the Critical Distance DcD_c where direct sound equals reverberant sound, and estimate Peutz %ALcons\%AL_{\text{cons}} speech intelligibility.

Venue Acoustics Presets
SABINE / EYRING RT60 DECAYRT60RT_{60}
1.20s (Eyring)
Sabine: 1.35 sSabins: 238 m²
CRITICAL DISTANCE (DIRECT = REVERB)DcD_c
3.93m
Direct-to-Reverb @ 12m: -4.7 dBQ = 8
ARTICULATION LOSS OF CONSONANTS%ALcons\%AL_{\text{cons}}
2.6%
Rating: EXCELLENTVol: 2002 m³
ARCHITECTURAL VOLUME, ABSORPTION & DIRECTIVITY
m
5 m60 m
m
4 m40 m
m
2.5 m20 m
Sabin/m²
0.04 Sabin/m²0.85 Sabin/m²
Q
1 Q30 Q
m
1 m50 m
ENERGY DECAY (−60 dB) & DIRECT-TO-REVERBERANT FIELD CROSSOVER
Direct Sound Field (−6dB/dbl)Reverberant Field FloorTotal Combined Room SPL
IMPULSE DECAY SLOPE (−60 dB RT60)0dB-15dB-30dB-45dB-60dBEyring RT60: 1.20 sSabine RT60: 1.35 sCRITICAL DISTANCE Dc CROSSOVER (1m – 50m)Dc = 3.9mListener (12m)
Max Intelligible Throw Limit (3.16 × Dc): 12.4 mBeyond 12.4m, deploy delayed fill speakers!
HOW IT WORKS: ELECTRO-ACOUSTIC PHYSICS & MATHEMATICAL DERIVATION

Sabine vs. Eyring Reverberation Physics & Critical Distance (Dc)

Reverberation time (RT60RT_{60}) defines the duration required for an interrupted steady-state sound field in an enclosed space to decay by 60 dB60\text{ dB} (one-millionth of its initial acoustic energy). Wallace Sabine’s classic 1898 empirical equation assumes a lightly damped diffuse room (αˉ<0.25\bar{\alpha} < 0.25). For acoustically treated rooms with higher absorption, Carl Eyring’s logarithmic formulation accounts for discrete step-wise energy loss at each reflection boundary.

As a listener moves away from a loudspeaker of directivity factor QQ, the direct sound decays at −6 dB-6\text{ dB} per doubling of distance, while the diffuse reverberant energy remains approximately constant throughout the hall. The distance at which Direct Sound Pressure equals Reverberant Sound Pressure (0 dB0\text{ dB} direct-to-reverberant ratio) is the **Critical Distance (DcD_c)**.

Sabine & Eyring-Norris Reverberation Time EquationsEQ-01
RT60,Sabine=0.161⋅VS⋅αˉ,RT60,Eyring=0.161⋅V−Sln⁡(1−αˉ)RT_{60,\text{Sabine}} = \frac{0.161 \cdot V}{S \cdot \bar{\alpha}}, \qquad RT_{60,\text{Eyring}} = \frac{0.161 \cdot V}{-S \ln(1 - \bar{\alpha})}
Critical Distance (Dc) & Peutz Articulation Loss (%ALcons)EQ-02
Dc=0.141Q⋅Rπ≈0.057Q⋅VRT60,%ALcons≈200⋅d2⋅RT602V⋅QD_c = 0.141 \sqrt{\frac{Q \cdot R}{\pi}} \approx 0.057 \sqrt{\frac{Q \cdot V}{RT_{60}}}, \qquad \%AL_{\text{cons}} \approx \frac{200 \cdot d^2 \cdot RT_{60}^2}{V \cdot Q}

Nomenclature & Physical Variables

  • VV
    Total enclosed room volume
    Unit: m³
  • SS
    Total internal boundary surface area of walls, floor, and ceiling
    Unit: m²
  • αˉ\bar{\alpha}
    Area-weighted mean acoustic absorption coefficient (0<αˉ<10 < \bar{\alpha} < 1)
    Unit: Sabin/m²
  • QQ
    Loudspeaker axial directivity factor
    Unit: dimensionless
  • DcD_c
    Critical Distance where Direct SPL equals Reverberant SPL
    Unit: m
FOH & System Tech Field Application Notes
  • In highly reverberant spaces (churches, train stations, gymnasiums) where you cannot add acoustic treatment, the ONLY way to increase Critical Distance DcD_c from the PA is to increase loudspeaker directivity QQ (using tight horns or steerable column line arrays) or deploy distributed delay speakers closer to the listeners.
  • According to V.M.A. Peutz, speech intelligibility degrades rapidly once listener distance exceeds 3.16×Dc3.16 \times D_c (where reverberant energy exceeds direct sound by +10 dB+10\text{ dB}).