room-acoustics

name	room-acoustics
description	Room acoustics design — reverberation time (Sabine/Eyring T60), absorption coefficients (NRC, SAA), room modes (axial, tangential, oblique), speech intelligibility (STI, RASTI, C80), noise criteria (NC, RC, NR curves), HVAC noise in rooms, isolation flanking paths, sound diffusion (QRD, skyline diffusers), flutter echo, early decay time (EDT), concert hall acoustics (LEDE, shoebox, vineyard), classroom acoustics (ANSI S12.60), and room acoustic simulation (ODEON, EASE).
metadata	{"priority":7,"promptSignals":{"phrases":["room acoustics","reverberation time","Sabine formula","speech intelligibility","acoustic treatment","room modes"],"minScore":3}}

Room Acoustics Design — Complete Skill

Reverberation Time

Sabine Formula

Reverberation time T60: T60 = 0.161 × V / (A_total) [s; V = room volume [m³]; A_total = total absorption [m²]] T60 = 0.161 × V / (S × ᾱ) [ᾱ = average absorption coefficient; S = total surface area [m²]]

Sabine limitation: valid for well-distributed absorption; ᾱ ≤ 0.3 (lightly damped rooms)

Eyring formula (more accurate for highly absorbing rooms): T60 = 0.161 × V / (-S × ln(1 - ᾱ)) [more accurate for ᾱ > 0.3] As ᾱ → 1 (fully absorbing anechoic): T60 → 0 (Eyring gives finite T60; Sabine overestimates)

Air absorption (important for large rooms at high frequency): T60 = 0.161 × V / (A_surfaces + 4mV) [m = air absorption coefficient [m⁻¹]] m = 0 at 500 Hz; m ≈ 0.001–0.008 m⁻¹ at 2,000–8,000 Hz (depends on humidity)

Target Reverberation Times

By room type:

Room Type	T60 at 500 Hz	Notes
Recording studio	0.2–0.4 s	Dead; controlled; live + dead sections
Speech/broadcast studio	0.3–0.5 s	Clear speech; minimal coloration
Conference room	0.4–0.7 s	Good clarity; some warmth
Classroom	0.4–0.6 s	ANSI S12.60 max 0.6 s for < 283 m³
Open office	0.3–0.5 s	Short RT for privacy; absorbing ceiling
Cinema	0.3–0.6 s	Optimized for reproduced sound
Opera/concert hall	1.4–2.2 s	Long for music richness; full hall
Worship (speech-focused)	0.8–1.2 s	Compromise
Worship (organ/choir)	1.5–3.0 s	Long for reverberant music
Gymnasium	1.0–1.5 s	Needs treatment for speech intelligibility

Frequency dependence: Bass (125 Hz): RT typically 20–50% longer than 500 Hz (acceptable); if too long → muddy bass Treble (4,000 Hz): RT shorter due to air absorption (natural); acceptable

Absorption Materials

Absorption Coefficients (NRC)

Noise Reduction Coefficient (NRC): NRC = average of α at 250, 500, 1,000, 2,000 Hz [dimensionless; 0 = perfect reflector; 1 = perfect absorber]

Common materials:

Material	NRC	α_125	α_500	α_2000	Notes
Acoustic ceiling tile (Armstrong Cirrus)	0.90	0.35	0.90	0.95	Standard suspended ceiling
Open-cell foam 50 mm	0.75	0.15	0.75	0.95	High frequencies
Fiberglass board 50 mm, 64 kg/m³	0.90	0.40	0.95	0.95	Excellent broadband
2" thick fiberglass, 32 kg/m³	0.80	0.25	0.85	0.95	Common wall treatment
Carpet (medium pile)	0.35	0.05	0.30	0.60	Low frequencies poor
Curtain (medium weight)	0.35	0.05	0.35	0.60	Low freq poor
Concrete block (unpainted)	0.35	0.30	0.40	0.35	Mid frequencies
Bare concrete	0.02	0.01	0.02	0.02	Hard reflective
Glass (window)	0.10	0.25	0.06	0.02	High frequencies reflective
Wood panel, 10mm	0.15	0.30	0.10	0.08	Panel absorber; bass

SAA (Sound Absorption Average): newer metric; average of 12 third-octave bands 200–2,500 Hz

Total Absorption Calculation

Sabine absorption units: A_i = α_i × S_i [m²; S_i = area of material i; A_i = sabins (m²)] A_total = Σ A_i [total absorption; substitute into Sabine formula]

Example (conference room V = 200 m³): Floor: 40 m² carpet α = 0.30 → A = 12 m² Ceiling: 40 m² tile NRC 0.70 → A = 28 m² Walls: 100 m² gypsum α = 0.05 → A = 5 m² T60 = 0.161 × 200 / 45 = 0.72 s (target 0.5 s → need more absorption) Add 20 m² acoustic panels (α = 0.90) on walls: A_panels = 18 → A_total = 63 → T60 = 0.51 s ✓

Room Modes (Standing Waves)

Axial, Tangential, Oblique Modes

Room mode frequencies: f_nml = c/2 × √((n/L)² + (m/W)² + (l/H)²) [Hz; n,m,l = mode indices; L,W,H = room dimensions; c = 343 m/s] Axial modes (one index ≠ 0): f = c×n/(2L) etc.; strong (most problematic) Tangential modes (two indices ≠ 0): weaker Oblique modes (three indices ≠ 0): weakest

Axial mode example (room 5 × 4 × 3 m): f_100 = 343/(2×5) = 34.3 Hz; f_200 = 68.6 Hz; f_010 = 42.9 Hz; f_001 = 57.2 Hz

Modal density (Schroeder criterion): Above f_Schroeder = 2,000 × √(T60/V): modes dense → diffuse field (statistical treatment valid) Below f_Schroeder: individual modes dominate → lumped acoustic analysis

Mode spacing criterion (Bolt): Axial modes should be evenly distributed; avoid coincident modes (room dimension ratios) Best room ratios: L:W:H ≈ 1.0:1.28:1.54 (Bolt's "golden" ratios); avoids mode clustering

Bass trap: For recording studios: place bass-absorbing material (mineral wool 200 mm thick) in corners (pressure maxima for many axial modes) Limp mass panel absorber: tuned to peak at 80–150 Hz; complements porous absorber

Speech Intelligibility

Speech Transmission Index (STI)

STI range: 0.0–0.30: bad (unintelligible); 0.30–0.45: poor; 0.45–0.60: fair; 0.60–0.75: good; 0.75–1.0: excellent Classrooms: STI ≥ 0.75 (ANSI S12.60 requirement)

STI depends on: T60 (long RT → low STI): STI ≈ K/(1 + 14×t_lag) [Houtgast & Steeneken; simplified] Signal-to-noise ratio: each 3 dB SNR improvement → significant STI improvement SNR ≥ 15 dB for good intelligibility; SNR < 5 dB → poor

C80 (clarity index): C80 = 10 × log₁₀(E_80/E_late) [E_80 = sound energy in first 80 ms; E_late = energy after 80 ms] Music: C80 = -2 to +2 dB (good clarity with warmth); C80 > +4 dB → too dry for music

D50 (definition): D50 = E_50/(E_total) × 100% [percentage of energy in first 50 ms; speech clarity] Speech: D50 > 50% desirable; concert music: D50 = 20–40% (more late energy preferred)

Noise Criteria

NC and RC Curves

NC (Noise Criteria) curves: Define acceptable background noise spectrum for different uses NC rating = value of NC curve that just touches octave-band SPL spectrum from below

NC targets:

Space	NC target
Broadcast studio	NC-15 to NC-20
Concert hall	NC-15 to NC-25
Conference room	NC-25 to NC-35
Open office	NC-35 to NC-45
Classroom	NC-30 to NC-40 (ANSI S12.60: ≤ 35 dBA)
Restaurant	NC-40 to NC-50

RC (Room Criteria) curves: More complete than NC; includes low-frequency content; preferred for HVAC noise assessment RC-25: good quality office; RC-35: acceptable; RC-45: background noise just noticeable

Sound Diffusion

Diffuser Types

QRD (Quadratic Residue Diffuser, Schroeder): Wells of varying depths based on quadratic residue sequences; scatters sound hemispherically Design frequency f_d = c / (2 × w_well) [w_well = well width]; effective above f_d Period width: minimum D_min = D × N [N = sequence length; D = well width = λ_design/2]

Skyline diffuser: 2D QRD; different heights in both directions → scatters in full hemisphere Used on rear walls and ceiling of recording studios; treatment of control room rear wall

Installation: Minimum distance from diffuser: 1–2 m for diffuse field region Mix with absorbers: too much diffusion → live room; too much absorption → dead room

LEDE (Live End Dead End) recording studio: Front (dead end): absorptive treatment → no early reflections from front wall Rear (live end): diffusive treatment → rich, diffuse late reflections → natural room sound

Concert Hall Acoustics

Key parameters: T60 (mid-frequency): 1.8–2.2 s (full hall); EDT = early decay time (first 10 dB, ×6); EDT ≈ T60 for diffuse IACC (Inter-Aural Cross-Correlation): measure of spaciousness; lower IACC → more immersive; IACC < 0.5 desired Clarity C80: -2 to +2 dB (balance clarity and warmth) G (Strength/Gain): 4–8 dB at 500 Hz (reinforcement relative to free field)

Hall shapes: Shoebox: parallel side walls reflect → high IACC (narrow); good for classical music; Vienna Musikverein model Vineyard/terrace: side balconies at various angles → lower IACC; good spaciousness; Berlin Philharmonie Fan: wide; poor lateral reflections; low G; avoid for classical music

Standards and References

Standard	Scope
ANSI S12.60	Classroom acoustics (T60 ≤ 0.6 s; background noise ≤ 35 dBA)
ISO 3382-1	Measurement of room acoustic parameters (T60, EDT, C80, STI)
ASHRAE 2019 HVAC Applications Handbook	Chapter 48: Sound and vibration control in buildings
IEC 60268-16	STI measurement standard
BB93 (UK)	Acoustic design of schools
ASTM C423	Sound absorption coefficient by reverberation room method

Output

Provide: room description (V [m³]; L × W × H [m]; use: speech/music/studio/classroom), current surface finishes and areas (with α values from ASTM C423 database at 125, 250, 500, 1,000, 2,000, 4,000 Hz), Sabine T60 calculation (at 500 Hz; table for 125–4,000 Hz octave bands), target T60 [s] (by room type; per ANSI S12.60 or ISO 3382), additional absorption required ΔA [m²] (type and location: ceiling/walls; NRC of selected material), room modes (3 lowest axial modes in each dimension [Hz]; Schroeder frequency [Hz]; bass trap recommendation), background noise (existing NC level; NC target; HVAC noise contributor; isolation requirement), speech intelligibility (estimated STI or D50; T60 + SNR combined assessment), diffusion (if recording studio/concert hall: QRD specification; f_design [Hz]; well depth [mm]; location), and applicable standard (ANSI S12.60, ISO 3382-1, ASHRAE Chapter 48).