From reverberation time and room modes to transmission loss and noise criteria - the complete engineering
reference for architectural acoustics, studio design, and soundproofing.
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.
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
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
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.
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 dimensionSchroeder frequency: f_s ≈ 2000√(RT60/V) - above this, modal response is smooth
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.
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.
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-35Office (open plan): NC-35 to NC-40 | Restaurant / retail: NC-40 to NC-50Mechanical / 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):
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.