acoustics-nvh

name	acoustics-nvh
description	Acoustics and NVH — sound pressure level (dB), octave bands, sound power, transmission loss, absorption, room acoustics (RT60), noise source ranking, sound intensity, STC ratings.
metadata	{"priority":7,"promptSignals":{"phrases":["acoustics","NVH","sound pressure","decibel","noise","transmission loss","sound power","absorption","RT60","SPL"],"minScore":3}}

Acoustics & NVH — Complete Skill

Fundamental Quantities

Sound Pressure Level (SPL)

L_p = 20 log₁₀(p_rms / p_ref) [dB] p_ref = 20 μPa (threshold of hearing, air) p_ref = 1 μPa (underwater acoustics)

SPL [dB]	Source
0	Threshold of hearing
30	Quiet library
60	Normal conversation (1m)
85	Heavy traffic — OSHA limit (8hr)
100	Chainsaw at 1m
120	Pain threshold
140	Jet engine (30m)

Addition of incoherent sources: L_total = 10 log₁₀(Σ 10^(L_i/10)) [dB] Two equal sources: L_total = L₁ + 3 dB (not doubled!)

Sound Power Level (SWL)

L_W = 10 log₁₀(W / W_ref) [dB] W_ref = 10⁻¹² W L_p = L_W - 10 log₁₀(4πr²) [free field, point source, anechoic] L_p = L_W + 10 log₁₀(Q/(4πr²) + 4/R) [reverberant field, Q = directivity, R = room constant]

Frequency Bands

1/1 octave bands: 31.5, 63, 125, 250, 500, 1k, 2k, 4k, 8k, 16k Hz 1/3 octave bands: 20 bands per decade Center frequencies: 25, 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1k, 1.25k, 1.6k, 2k, 2.5k, 3.15k, 4k, 5k, 6.3k, 8k, 10k, 12.5k Hz

Frequency Weighting

A-weighting (dBA): correlates to human hearing sensitivity (peaks ~3-4 kHz) A(f) = 12200² f⁴ / [(f²+20.6²)(f²+12200²)√(f²+107.7²)(f²+737.9²)] Standard for occupational noise exposure

C-weighting (dBC): flat 20Hz-20kHz — peak sound pressure Z-weighting: unweighted (linear), all frequencies equal

Propagation

Inverse Square Law (Free Field, No Reflection)

ΔL = -20 log₁₀(r₂/r₁) dB [point source] Double distance → -6 dB; 10× distance → -20 dB

Atmospheric Absorption (ISO 9613-1)

Adds ≈ 0.5-10 dB/100m depending on frequency and humidity Significant above 1 kHz for long distances (>100m)

Barrier Attenuation (Maekawa)

IL = 10 log₁₀(3 + 20N) [dB] where N = 2δ/λ (Fresnel number) δ = path length difference (diffraction path vs. direct), λ = wavelength Practical: barriers give 5-20 dB insertion loss; more effective at high frequency

Sound Absorption

Absorption Coefficient α

α = (energy absorbed) / (energy incident) ∈ [0, 1] α = 0: perfect reflector (concrete, glass) α = 1: perfect absorber (open window)

Sabine absorption: A = Σ(α_i × S_i) [m² Sabin] Room constant: R = S × ᾱ / (1 - ᾱ) = A / (1 - ᾱ) ᾱ = average absorption coefficient = A/S_total

Typical α values (500 Hz)

Concrete floor: 0.02, Carpet: 0.35, Acoustic tile: 0.70-0.90, Open window: 1.0 Fiberglass batt (50mm): α ≈ 0.80 at 500 Hz; poor below 250 Hz (thickness/λ effect)

Porous absorbers: high α at high freq, low at low freq Resonant absorbers (Helmholtz): peak α at resonant frequency f_r = c/(2π) × √(S/(V_neck × L_eff))

Reverberation Time (RT60)

T₆₀ = time for 60 dB SPL decay after source stops

Sabine formula (low absorption, ᾱ < 0.2): RT60 = 0.161 × V / A [s] (V = room volume [m³], A = total absorption [m² Sabin])

Norris-Eyring (high absorption, ᾱ > 0.2): RT60 = 0.161 × V / (-S × ln(1-ᾱ))

Target RT60 by room type: Recording studio: 0.2-0.4 s Office: 0.5-0.8 s Concert hall: 1.5-2.5 s Cathedral: 4-8 s Classroom (good speech): 0.4-0.6 s

Transmission Loss (TL) — Partitions

Mass Law (Limp Wall)

TL = 20 log₁₀(m × f) - 47.5 [dB] (m = mass/area [kg/m²], f = frequency [Hz]) +6 dB per doubling of mass or frequency

Single leaf partition (typical): 100 kg/m² (100mm concrete): TL ≈ 45 dB at 500 Hz 25 kg/m² (gypsum board 25mm): TL ≈ 35 dB at 500 Hz

Coincidence Dip

At f_c (critical frequency): TL drops 10-15 dB f_c = c²/(1.8 × c_L × t) where c_L = √(E/ρ(1-ν²)), t = panel thickness Steel 2mm: f_c ≈ 12 kHz; concrete 100mm: f_c ≈ 300 Hz; gypsum 12mm: f_c ≈ 2500 Hz

Double-Leaf Wall

Air gap + resilient mounting → +5-15 dB vs. single leaf (avoids mass law limit) Mass-air-mass resonance: f₀ = 84/√((m₁+m₂) × d/(m₁×m₂)) [Hz] (d = gap [m]) Below f₀: TL follows total mass; above f₀: superior to mass law

STC (Sound Transmission Class) Rating

Single number from 125-4000 Hz TL curve fit to standard contour STC 25: loud speech understood through wall STC 40: loud speech barely heard STC 50: loud speech not audible STC 55+: excellent isolation (studios, hotels)

ASTC: Apparent STC — includes flanking transmission (always lower than STC)

NVH Engineering

Vibro-Acoustic Transfer Path Analysis (TPA)

Total noise = Σ_i (force at source i) × (transfer function H_i from source to receiver) Identify: which source path contributes most → target with isolation/damping

Blocked force: force at interface with rigid blocking — interface-independent Modern TPA: characterize source by blocked forces, structure by mobility FRFs

Noise Source Ranking

Measure sound intensity (I = p × v [W/m²]) close to each source surface L_I = 10 log₁₀(I/I_ref) [dB], I_ref = 10⁻¹² W/m² Sound power from surface: W = ∫I·dA Rank surfaces/components by contribution → focus treatment on top contributors

Structure-Borne Noise

Vibration → radiated sound: L_p = L_v + 20 log₁₀(σ_rad) + 20log₁₀(ρc/ρ_s c_L) σ_rad = radiation efficiency (0.01 for subsonic bending, 1 for surface above coincidence) Reduce: damping (CLD — constrained layer), mass, decoupling

CLD (Constrained Layer Damping)

Viscoelastic layer + constraining layer on panel surface Loss factor η: 0.1-0.4 (broadband) — much better than free-layer damping Effective above glass transition of viscoelastic: η peaks at T_g temperature

OSHA Noise Exposure Limits (29 CFR 1910.95)

Duration [hr/day]	Max SPL [dBA]
8	90
4	95
2	100
1	105
0.5	110
0.25	115 (never exceed)

Dose method: D = Σ(C_i/T_i) ≤ 1 (C = actual exposure time, T = allowable duration)

Output

Provide: SPL at receiver [dBA], sound power L_W [dB], RT60 [s], TL/STC rating, NRC (noise reduction coefficient), dominant source identified, recommended treatment (absorption coefficient, mass added, CLD location).