Acoustics & Soundproofing

From reverberation time and room modes to transmission loss and noise criteria - the complete engineering reference for architectural acoustics, studio design, and soundproofing.

All Topics

Reverberation Time Calculator - RT60 (Sabine & Eyring)

Formulas
Sabine: RT60 = 0.161·V / A  |  Eyring: RT60 = 0.161·V / [−S·ln(1−αm)]
V Room Volume (m³)
A Total Absorption (sabins, m²)
S Total Surface Area (m²) - for Eyring
αm Mean Absorption Coeff. (0–1) - for Eyring
RT60
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Sound Pressure & Power Level Calculator

Formulas
Lp = 20·log(p / 20μPa)  |  Lw = 10·log(W / 10⁻¹² W)
p Sound Pressure (Pa)
W Sound Power (W)
Sound Levels
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Room Mode Frequency Calculator (Axial, Tangential, Oblique)

Formula
f = (c/2) × √[(nx/Lx)² + (ny/Ly)² + (nz/Lz)²]   c = 343 m/s
Lx Room Length (m)
Ly Room Width (m)
Lz Room Height (m)
Mode orders (nx, ny, nz) - comma separated
Modal Frequency
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Transmission Loss Calculator (Mass Law)

Formula (Field Incidence Mass Law)
TL ≈ 20·log(m·f) − 47.5  (dB)
m Surface mass density (kg/m²)
f Frequency (Hz)
Transmission Loss
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NRC / SAA Calculator (from Octave Band Absorption Coefficients)

Formula
NRC = (α250 + α500 + α1k + α2k) / 4
α at 125 Hz
α at 250 Hz
α at 500 Hz
α at 1000 Hz
α at 2000 Hz
α at 4000 Hz
NRC / SAA
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Noise Criterion (NC) Estimator - Octave Band SPL

Method (ASHRAE / ANSI S12.2)
NC = lowest NC curve not exceeded in any octave band (63–8000 Hz)
SPL at 63 Hz (dB)
SPL at 125 Hz (dB)
SPL at 250 Hz (dB)
SPL at 500 Hz (dB)
SPL at 1000 Hz (dB)
SPL at 2000 Hz (dB)
SPL at 4000 Hz (dB)
SPL at 8000 Hz (dB)
Estimated NC Rating
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1 Soundproofing & Isolation Metrics

Soundproofing performance is measured by standardised ratings that quantify how much airborne or impact sound a construction assembly attenuates. The most widely used in the English-speaking world are STC (airborne) and IIC (impact), while ISO countries use Rw and Ln,w respectively. Understanding these ratings is essential for specifying walls, floors, and ceilings in residential, commercial, and studio construction.

Sound Transmission Class (STC) is a single-number rating of an assembly's ability to reduce airborne sound. It is derived from laboratory measurements across 16 one-third octave bands from 125 Hz to 4000 Hz, plotted against a reference contour. The STC number is the value of the reference contour at 500 Hz after fitting. Higher STC means better isolation. STC 25 means normal speech is easily understood through a partition; STC 45 means loud speech is heard but barely intelligible; STC 60 means even a loud shout is barely audible.

Impact Insulation Class (IIC) measures floor/ceiling resistance to structure-borne impact noise - footsteps, dropped objects, chair scraping. A bare concrete slab may achieve IIC 28; add carpet and pad and it rises to IIC 65+. Building codes typically require IIC 50 minimum for multi-family residential floors.

STC Rating Scale - What You Hear Through the Wall 25 Loud speech understood 35 Loud speech audible 45 Loud speech barely audible 55 Good speech privacy 65 Near-total isolation Code min (STC 50 apt.) Typical assemblies: Single drywall (STC 33) | Double drywall (STC 43) | Staggered stud wall (STC 55) | Double leaf + mass loaded vinyl (STC 65+)
Figure 1: STC scale with subjective descriptions and typical assembly ratings. Note that field measurements (FSTC) are typically 3–5 points lower than lab values due to flanking transmission through connected structures.
Metric
Standard & Target
STC / IIC
ASTM E413 / E989 - STC 50+, IIC 50+ (residential)
Rw / Ln,w
ISO 717-1 / 717-2 - metric equivalent of STC/IIC
FSTC / FIIC
Field versions - typically 3–5 lower due to flanking
CAC
Ceiling Attenuation Class - CAC 35+ open-plan offices
OITC
Outdoor-Indoor TC - lower frequencies (traffic, aircraft)
ΔIIC
Floor treatment improvement - carpet, floating floor
Flanking is the enemy of field performance. Even a perfectly isolated wall achieves nothing if sound travels through the floor slab, ceiling plenum, or shared ductwork. Real-world FSTC values are consistently 3–8 points lower than lab STC. Addressing flanking paths - resilient channels, acoustic isolation clips, floating floors - is often more important than the wall assembly itself.

2 Reverberation Time - RT60, EDT & the Sabine/Eyring Equations

Reverberation time (RT60) is the time it takes for a sound to decay 60 dB after the source stops. It is the single most important parameter in room acoustics, governing speech intelligibility, music clarity, and the overall character of a space. A cathedral may have RT60 of 8–10 seconds; a recording studio control room targets 0.2–0.4 seconds; a classroom should sit between 0.4–0.6 seconds for good speech intelligibility.

Sabine's formula (1900) - RT60 = 0.161·V/A - works well for rooms with relatively low average absorption (αm < 0.3). The total absorption A is the sum of each surface area multiplied by its absorption coefficient at the frequency of interest: A = Σ(Si·αi). The 0.161 constant is derived from the speed of sound (343 m/s at 20°C) and assumes a perfectly diffuse field.

Eyring's formula is more accurate at higher absorption levels and avoids predicting negative RT60: RT60 = 0.161·V / [−S·ln(1−αm)]. For αm < 0.2, both formulas give nearly identical results. For αm > 0.5 (heavily treated rooms), Sabine significantly over-predicts RT60 and Eyring should be used.

RT60 = 0.161 × V / A
V = room volume (m³) | A = Σ(Si·αi) = total absorption (sabins/m²) αi = absorption coefficient of surface i (0–1 per octave band) Eyring: RT60 = 0.161·V / [−S·ln(1−αm)] for heavily treated rooms
Space Type
Target RT60 (mid-freq.)
Recording studio (control room)
0.2 – 0.4 s
Broadcast / podcast studio
0.2 – 0.35 s
Classroom / conference room
0.4 – 0.6 s
Open-plan office
0.5 – 0.8 s
Concert hall (orchestral)
1.8 – 2.2 s
Cathedral / large church
4 – 10 s
Early Decay Time (EDT) is often more perceptually relevant than RT60. It is derived from the initial 10 dB decay and is more sensitive to early reflections and room treatment near the listener. In a well-designed concert hall, EDT ≈ RT60. When EDT < RT60, the room feels drier and more intimate. ISO 3382 standardises measurement of both.
Worked Example 1

RT60 of a Recording Studio Live Room

Problem: A live recording room measures 8 m × 5 m × 3 m (L×W×H). The surfaces have the following mid-frequency (500 Hz) absorption: concrete floor (α=0.02, 40 m²), gypsum walls (α=0.06, 78 m²), acoustic panels covering 30% of wall area (α=0.85 replacing 0.06, 23.4 m²), acoustic ceiling (α=0.75, 40 m²). Calculate RT60 using Sabine's formula.
Step 1 - Total surface area & absorption contributions
V = 8 × 5 × 3 = 120 m³
Floor: A = 40 × 0.02 = 0.80 sabins
Untreated walls: A = (78 − 23.4) × 0.06 = 54.6 × 0.06 = 3.28 sabins
Acoustic panels: A = 23.4 × 0.85 = 19.89 sabins
Acoustic ceiling: A = 40 × 0.75 = 30.0 sabins
Total A = 0.80 + 3.28 + 19.89 + 30.0 = 53.97 sabins
Step 2 - Apply Sabine's formula
RT60 = 0.161 × V / A = 0.161 × 120 / 53.97
RT60 = 19.32 / 53.97 ≈ 0.36 s
Answer: 0.36 s - comfortably within the 0.3–0.5 s target for a live recording room. The ceiling treatment dominates, contributing 55% of total absorption. Note: this is a mid-frequency estimate; bass frequencies (125–250 Hz) will have considerably longer RT60 in this room and may require dedicated bass traps.

3 Room Modes - Resonance, Bass Buildup & Control

When sound waves reflect between parallel surfaces, they create standing waves at discrete frequencies called room modes. At these frequencies, the acoustic pressure distribution is uneven - some positions in the room have excessive bass (pressure maxima) while others have very little (pressure nulls). This is why you can walk around a room and hear the bass completely disappear in certain spots.

Room modes are categorised by the number of room dimensions involved. Axial modes involve one dimension only (e.g., 1,0,0 - length only) and are the strongest and most problematic. Tangential modes involve two dimensions and are 3 dB weaker. Oblique modes involve all three dimensions and are 6 dB weaker still. In a typical small room (studio, home theatre), the axial modes dominate below about 300 Hz.

f(nx,ny,nz) = (c/2) × √[(nx/Lx)² + (ny/Ly)² + (nz/Lz)²]
c = 343 m/s (speed of sound at 20°C) | nx, ny, nz = integer mode orders (0,1,2,...) Axial (1,0,0): f = c/(2·Lx) = 343/(2L) | First mode = half wavelength fits in dimension Schroeder frequency: f_s ≈ 2000√(RT60/V) - above this, modal response is smooth
Axial Room Mode - 1st Order (Half-Wavelength Standing Wave) Pressure node Max pressure Max pressure L = λ/2 → f = c/(2L)
Figure 2: First-order axial mode. One half-wavelength fits between the walls. Pressure maxima sit at the walls (antinodes); a pressure null (node) sits at the room centre. A subwoofer placed at the wall excites this mode maximally; a listener at the centre hears very little bass at this frequency.
Avoid cube rooms and simple integer ratios. A 4m × 4m × 4m room is the worst possible shape - all three axial modes coincide at 42.9 Hz, 85.7 Hz, etc., creating massive bass buildup. Recommended ratios (Bolt, EBU): 1 : 1.25 : 1.6 or 1 : 1.4 : 2.1. Acoustic treatment with bass traps at corners (where all modal pressure maxima meet) is the most effective remedy.
Worked Example 2

First Three Axial Modes of a Home Studio

Problem: A home studio is 5.2 m long × 3.6 m wide × 2.6 m high. Calculate the first axial mode in each dimension and identify any problematic coincidences.
First axial modes - f = c / (2L)
Length (5.2 m): f = 343 / (2 × 5.2) = 343 / 10.4 = 33.0 Hz
Width (3.6 m): f = 343 / (2 × 3.6) = 343 / 7.2 = 47.6 Hz
Height (2.6 m): f = 343 / (2 × 2.6) = 343 / 5.2 = 65.9 Hz
Check for coincidences (modes within 5 Hz of each other)
2nd length mode: 2 × 33.0 = 66.0 Hz ← coincides with height mode at 65.9 Hz!
Gap = 0.1 Hz - this modal coincidence will cause strong bass buildup ~66 Hz.
Answer: Length (33 Hz), Width (47.6 Hz), Height (65.9 Hz). The 2nd-order length mode (66 Hz) nearly perfectly coincides with the 1st-order height mode (65.9 Hz) - this will create a significant bass problem near 66 Hz. Bass traps in all four vertical corners (where both modes have pressure maxima) are strongly recommended. The Schroeder frequency for this room (assuming RT60 ≈ 0.4s) is approximately 2000 × √(0.4/48.7) ≈ 181 Hz - modal treatment is needed below this frequency.

4 Transmission Loss, Mass Law & Partition Design

Transmission Loss (TL) is the ratio, in decibels, of the sound power incident on one face of a partition to the power transmitted through it. Unlike STC (which is a single-number rating), TL is measured and specified at individual frequencies. Designing for TL requires understanding the mass law, the coincidence dip, and the effects of decoupling and air gaps.

The mass law states that for a single solid partition, TL increases by approximately 6 dB for every doubling of surface mass density, and by 6 dB per octave increase in frequency. A 12 mm plasterboard sheet (≈10 kg/m²) achieves roughly TL 30 dB at 500 Hz. Doubling the sheet gives ≈10 kg/m² more, adding ≈6 dB. This is why sheer mass - concrete, brick, dense board - is the simplest path to isolation.

The coincidence effect creates a dip in TL at the coincidence frequency, where the bending wavelength in the partition matches the acoustic wavelength. For standard 12 mm gypsum board, this occurs near 2,500 Hz. Above the coincidence frequency, TL improves at 10 dB/octave (better than mass law). Below it, mass law applies at 6 dB/octave.

TL ≈ 20·log(m·f) − 47.5  (dB)
m = surface mass density (kg/m²) | f = frequency (Hz) Normal incidence: TL = 20·log(m·f) − 42.5 (3 dB higher than field incidence) Double-leaf: add ~10–15 dB with decoupled leaves and cavity absorption
Single-Leaf Assemblies

Performance governed purely by mass. Resilient mounts add no benefit because there is no air gap. Practical limit around STC 40–45 for typical construction. Examples: single brick wall, 2× concrete block, single sheet heavy drywall.

Double-Leaf & Decoupled

Two independent leaves separated by an air gap. The gap acts as a spring-mass resonator, boosting performance dramatically above the resonant frequency. Cavity absorption (mineral wool) adds 3–8 dB. Resilient channels, staggered studs, and double stud walls exploit this principle.

Mass-Air-Mass resonance is the Achilles heel of double walls. Two panels separated by an air gap have a resonant frequency f₀ = (c/2π)·√(1/m₁ + 1/m₂)/d, where d is the gap width in metres. Below f₀, the double wall actually performs worse than mass law. To push f₀ below the frequency range of interest, increase gap width and/or panel mass. A 100 mm cavity between two 15 mm drywall sheets gives f₀ ≈ 58 Hz.

5 Acoustic Absorption - Coefficients, NRC & Material Selection

Acoustic absorption converts sound energy into heat through friction in porous materials, or through panel and membrane resonance. The absorption coefficient α represents the fraction of incident sound energy absorbed by a surface at a given frequency. α = 0 means perfect reflection; α = 1 means total absorption (an open window). Real materials fall between these extremes, and α varies significantly with frequency.

The Noise Reduction Coefficient (NRC) is a single-number average of α at 250, 500, 1000, and 2000 Hz. It is the most commonly cited spec for acoustic foam, ceiling tiles, and panels. NRC 0.90 means the material absorbs 90% of sound energy at mid-frequencies. The Sound Absorption Average (SAA) extends this to 12 one-third octave bands from 200–2500 Hz and is preferred in ASTM E1374.

Material
NRC (approx.)
Bare concrete
0.02 – 0.05
Gypsum board (drywall)
0.05 – 0.10
Carpet on concrete
0.25 – 0.40
Open-cell acoustic foam (25mm)
0.50 – 0.70
Mineral wool board (50mm)
0.70 – 0.95
Suspended acoustic ceiling tiles
0.55 – 0.85
Bass trap (corner-mounted 100mm rockwool)
0.85 – 1.0 at mid/high; 0.3–0.6 at bass
Porous absorbers work at high frequencies; panel absorbers work at low frequencies. Acoustic foam and mineral wool are efficient mid/high-frequency absorbers - thin materials (25–50mm) offer little bass absorption. For low-frequency control (63–250 Hz), use thick mineral wool bass traps (>100mm) in room corners, membrane/panel absorbers, or Helmholtz resonators tuned to specific problem frequencies. A well-treated room needs both types working together.
Worked Example 3

NRC and Total Room Absorption for an Open-Plan Office

Problem: An open-plan office is 20 m × 15 m × 3 m (V = 900 m³). The ceiling (300 m²) has suspended acoustic tiles with α values: 250Hz=0.55, 500Hz=0.75, 1kHz=0.80, 2kHz=0.80, and the walls (210 m²) are gypsum with α = 0.06 across all bands. Calculate (a) the ceiling NRC, (b) total absorption at 500 Hz, and (c) predicted RT60 at 500 Hz.
(a) Ceiling NRC
NRC = (α250 + α500 + α1k + α2k) / 4 = (0.55 + 0.75 + 0.80 + 0.80) / 4
NRC = 2.90 / 4 = 0.73
(b) Total absorption at 500 Hz
Ceiling: A = 300 × 0.75 = 225 sabins
Concrete floor: A = 300 × 0.02 = 6 sabins
Walls: A = 210 × 0.06 = 12.6 sabins
Total A = 225 + 6 + 12.6 = 243.6 sabins
(c) RT60 using Sabine
RT60 = 0.161 × 900 / 243.6 = 144.9 / 243.6
RT60 = 0.59 s
Answer: Ceiling NRC = 0.73, Total A = 243.6 sabins, RT60 = 0.59 s. This is within the typical 0.5–0.8 s target for open-plan offices. However, at lower frequencies (250 Hz, where ceiling α drops to 0.55) RT60 will rise to approximately 0.78 s - still acceptable. The ceiling tiles contribute 92% of all absorption, illustrating how dominant ceiling treatment is in typical offices.

6 Noise Criteria - NC, NR & RC Curves

Background noise in buildings comes from HVAC systems, external traffic, mechanical plant, and occupants. Noise Criteria (NC) curves are the most widely used method for specifying and evaluating HVAC background noise in occupied spaces. Each NC curve represents a permissible spectrum of octave-band sound pressure levels from 63 Hz to 8000 Hz. A space "achieves" a given NC rating if its measured spectrum does not exceed the corresponding curve in any band.

The NC method was developed by Beranek (1957) and is widely referenced in ASHRAE and architectural standards. NR (Noise Rating) curves are the European equivalent, defined by ISO and used in the UK and Europe. Numerically they are similar but not identical. RC (Room Criteria) curves add a quality assessment - N (neutral), L (low-frequency rumble), H (high-frequency hiss) - making them more diagnostic for HVAC noise problems.

NC = lowest NC curve not exceeded at any octave band
Studio / recording booth: NC-15 to NC-20 | Bedroom / hotel: NC-25 to NC-35 Office (open plan): NC-35 to NC-40 | Restaurant / retail: NC-40 to NC-50 Mechanical / plant room: NC-55 to NC-65
Space
Recommended NC
Recording / broadcast studio
NC-15 to NC-20
Concert hall / opera house
NC-15 to NC-20
Classroom / conference room
NC-25 to NC-30
Private office
NC-30 to NC-35
Open-plan office
NC-35 to NC-40
Restaurant / lobby
NC-40 to NC-50
NC ratings below NC-20 demand extraordinary HVAC design. At NC-15 (the practical limit for critical listening rooms), air velocity in supply diffusers must stay below 1 m/s, and ductwork must be heavily lined and vibration-isolated. Even a single unlined elbow near the diffuser can push a studio from NC-15 to NC-30. Equipment noise, compressor vibration, and building structure-borne noise must all be addressed systematically.
Worked Example 4

NC Rating of a Boardroom HVAC System

Problem: Measured octave-band SPL in a boardroom (target NC-35): 63Hz=58, 125Hz=48, 250Hz=40, 500Hz=35, 1kHz=31, 2kHz=28, 4kHz=24, 8kHz=20 dB. What NC rating does this achieve, and which band is the limiting band?
Compare measured levels against NC curve limits

NC curve reference values (approximate, from ASHRAE Fundamentals):

NC-35: 63Hz=71 | 125Hz=55 | 250Hz=44 | 500Hz=36 | 1kHz=33 | 2kHz=31 | 4kHz=29 | 8kHz=28
NC-30: 63Hz=68 | 125Hz=51 | 250Hz=40 | 500Hz=32 | 1kHz=29 | 2kHz=27 | 4kHz=25 | 8kHz=24
Measured vs NC-30 limits:
250Hz: measured 40 = NC-30 limit 40 ✓ (just touches)
500Hz: measured 35 > NC-30 limit 32 ✗ (exceeds by 3 dB)
All bands vs NC-35: measured 35 (500Hz) < NC-35 limit 36 ✓ - all bands pass
Determine NC rating
NC rating = NC-35 (500 Hz is the limiting band at 35 dB)
Answer: NC-35. The 500 Hz band (35 dB) is the limiting factor - it exceeds the NC-30 curve by 3 dB but stays within NC-35. The boardroom meets the target NC-35 specification but is right at the boundary. To achieve NC-30, the 500 Hz content (typically from supply ductwork turbulence) would need to be reduced by at least 4 dB - achievable with a lined duct extension or lower diffuser velocity.