acoustic-enclosure

name	acoustic-enclosure
description	Acoustic enclosure design — insertion loss, transmission loss (mass law), coincidence frequency, damping, leakage, vibration isolation, OSHA/ISO limits, NR/NC curves.
metadata	{"priority":7,"promptSignals":{"phrases":["acoustic enclosure","noise enclosure","sound enclosure","transmission loss","mass law acoustics","noise control","insertion loss"],"minScore":3}}

Acoustic Enclosure Design — Complete Skill

Fundamentals

Sound pressure level: SPL = 20 log₁₀ (p/p_ref) [dB; p_ref = 20 μPa] Sound power level: L_W = 10 log₁₀ (W/W_ref) [dB; W_ref = 10⁻¹² W] Sound intensity level: L_I = 10 log₁₀ (I/I_ref) [dB; I_ref = 10⁻¹² W/m²]

Addition of levels (incoherent sources): L_total = 10 log₁₀ (Σ 10^(L_i/10)) [dB]

Noise Limits

OSHA (29 CFR 1910.95): 85 dBA → 8 hrs; 90 dBA → 8 hrs; 95 dBA → 4 hrs; 100 dBA → 2 hrs TWA = 90 dB action level; 85 dB recommended limit

ISO 1999: dose-response model for hearing damage NC curves: NC-20 to NC-65; for office, HVAC, machinery environments NR curves: European equivalent to NC; NR-25 to NR-75

Insertion Loss (IL)

Insertion Loss = SPL without enclosure - SPL with enclosure [dB] Effective IL depends on: Transmission Loss (TL) of panels, leakage, internal absorption

Required IL: IL_required = L_source - L_target [dB] L_source = SPL at 1 m from machine without enclosure

Transmission Loss — Mass Law

For homogeneous panel (forced field): TL = 20 log₁₀(f × m) - 47.5 [dB; f in Hz, m = surface density in kg/m²]

Examples at 1000 Hz: 12 mm steel (m = 94 kg/m²): TL = 20 log(1000 × 94) - 47.5 = 52 dB 25 mm dense concrete (m = 60 kg/m²): TL ≈ 48 dB 50 mm plywood (m = 30 kg/m²): TL ≈ 42 dB

Limitations: Below critical frequency: stiffness-controlled (TL better than mass law) At critical frequency: coincidence dip → TL drops significantly Above critical frequency: back to mass law + damping dependent

Coincidence (Critical) Frequency

f_c = c₀² / (1.8 c_L t) [Hz]

c₀ = 343 m/s (air); c_L = longitudinal wave speed in panel; t = panel thickness [m] c_L = √(E/ρ(1-ν²)) × correction

For steel: f_c ≈ 12,700/t [Hz; t in mm] (f_c = 1270 Hz for 10 mm steel) For aluminum: f_c ≈ 12,400/t For gypsum: f_c ≈ 3000/t

Coincidence dip magnitude: 10–20 dB below mass law Mitigation: add damping (CLD — constrained layer damping); use double panels with air gap

Double-Panel Wall

TL_double = TL₁ + TL₂ + ΔTL_airspace - 6 [dB]

Resonance dip: at frequency f_res = c₀/(2d) where d = airspace depth f_res = 343/(2 × 0.1) = 1715 Hz for 100 mm airspace

Absorption in cavity: use mineral wool → suppresses resonance modes → +10–15 dB

Double wall advantage: +15–20 dB over single wall of same total mass

Leakage — Critical Limitation

Sound leaks through gaps, penetrations, doors, ventilation openings Leakage reduction:

TL_effective = TL_total - 10 log₁₀ [1/(1-S_l/S_total) × (S_l/S_total) × 10^(TL/10)] Simplified: even 1% leakage limits effective TL to ~20 dB

Sealing: compression foam gaskets; labyrinth seals for large gaps; acoustic caulk for construction gaps

Ventilation: requires acoustic duct silencers; line duct with absorber; design f_pass > max important frequency

Internal Absorption

Absorption reduces reverberant buildup inside enclosure → reduces average SPL by: ΔL = 10 log₁₀ (R₀/R) where R = room constant before/after absorption R = α_avg × S_total / (1 - α_avg) [m²; α = absorption coefficient]

Absorption materials: Mineral wool (50 mm): α ≈ 0.7–0.95 at 500–4000 Hz Polyurethane foam (25 mm): α ≈ 0.4–0.8 at 500–4000 Hz Hanging baffles: very effective for high bay spaces

Vibration Isolation of Machine

Enclosure must be isolated from machine vibration or structure-borne sound regenerates: Isolators: rubber mounts or spring-damper beneath machine Static deflection δ: f_n = (1/2π)√(g/δ); isolate above 1.5 × f_n Transmissibility: T = 1 / |1-(f/f_n)²| → T < 0.1 requires f > 3 f_n

Design Procedure

1. Measure source L_p spectrum (octave bands 63–8000 Hz)
2. Determine required IL per band from limit
3. Calculate TL_required ≥ IL + 6 (leakage and room factor)
4. Select panel mass for mass law TL
5. Check coincidence and add CLD damping if needed
6. Design double panel if single panel TL inadequate (thick walls impractical)
7. Seal all penetrations; design ventilation with silencers
8. Add 50 mm mineral wool internally for reverberation control
9. Isolate machine from enclosure structure

Output

Provide: required IL [dB(A)] and per octave band, panel construction and TL [dB per band], estimated effective TL with leakage factor, coincidence frequency and mitigation, internal absorption area [m²], ventilation silencer insertion loss, A-weighted SPL at operator position.