Acoustic treatment and soundproofing

Treatment controls what you hear inside a room — absorbers shorten the reverberation and tame reflections, bass traps work on the low-frequency modes, diffusers scatter sound rather than swallowing it. Soundproofing is a different job: keeping sound from getting through the walls, which takes mass, airtightness and decoupling, not foam. This tool covers both. It models each absorber and diffuser, shows how to build it, adds the panels to a room, and estimates the transmission loss of a wall. The room’s modes, the basic RT60 calculator and the decibel maths are in room acoustics. Where to put the panels (first reflections, corners, the listening position) is covered by room placement.

How to use it

Porous absorbers. Pick a product, or type a flow resistivity σ, and set the thickness and the air gap behind the panel. The plot shows the absorption coefficient α against frequency at normal incidence, random incidence (Paris’s integral over 0–90°), or field incidence (0–78°). The dashed curve is the same panel flat on the wall, so you can see what the gap gains. The dotted curve uses the other impedance model. The λ/4 marker is c/(4·(d + gap)), and above it the panel is close to fully effective. The octave table gives the values the planner uses, and an NRC.
Bass traps and resonators. Choose a membrane (a plywood or MDF sheet over a sealed air cavity) or a perforated or slotted face (a Helmholtz resonator). Set the sheet, the cavity depth and the fill. The figures give f₀ from the textbook formula, the peak and the half-absorption bandwidth from the full model, and Q. Build it draws the box in front view and in section, and gives a cut list as CSV.
Diffusers. Choose a QRD (sₙ = n² mod N), a primitive-root diffuser (sₙ = gⁿ mod N) or a 2-D skyline (sₙₘ = (n² + m²) mod N), a prime N, the design frequency and the highest frequency. Depths are dₙ = sₙ·λ₀/(2N) and the well width is λmin/2. The polar plot compares the diffuser with a flat panel of the same width. Move the frequency slider to find where it works, and where it fails at the flat-plate frequencies N·f₀. A second plot shows the normalised diffusion coefficient against frequency. The cut list counts the fins and the blocks for each depth.
Room planner. Enter the room size and its surfaces (the material list from the acoustics tool), existing patches such as windows and sofas, and a room type for the target. Then add treatments: your designs from the first three tabs, or a product preset, with a count, a size and the surface they go on. The plot and table show RT60 by octave band before and after (Sabine and Eyring) against the target range. The tool says roughly how many more panels each band needs.
Soundproofing. Build each leaf from layers (gypsum, OSB, plywood, MLV, cement board, glass, masonry), tick Green Glue between layers if you use it, and choose the construction: one leaf, wood or steel studs, staggered studs, resilient channel, or double studs. Then set the cavity depth and the fill. You get a third-octave TL curve with the STC contour fitted, the STC, Rw (C; Ctr), the coincidence and mass–air–mass frequencies, and what a door and gaps in the wall do to it. A flanking checklist follows. Load any of the published assemblies to compare.

Method and assumptions

Porous materials are modelled by their characteristic impedance and wavenumber from Delany & Bazley (1970), with X = ρ₀f/σ, Zc = ρ₀c₀(1 + 0.0571X^−0.754 − j0.087X^−0.732), and from Miki (1990). Each layer is a transfer matrix on a rigid wall: Z = Zc·(Z_b + jZc·tan kd)/(Zc + jZ_b·tan kd). At oblique incidence the trace wavenumber carries through (extended reaction). Random-incidence α is Paris’s formula α = ∫α(θ)·sin 2θ dθ. Delany–Bazley is fitted for 0.01 ≤ X ≤ 1, and the tool warns when you leave that range.
Flow resistivities for the products are typical values from published measurements, not manufacturer specifications, which rarely give them. Owens Corning 703 is taken as about 19 000 Pa·s/m², 705 as 45 000, Rockwool Safe’n’Sound and RWA45 as about 10 000, and AFB as 12 000. Batches vary by ±30 %.
Model vs data sheet. Laboratory (Sabine) absorption coefficients come from a 6–10 m² sample in a reverberation room, and they exceed the infinite-panel prediction because of edge diffraction. That is why 2″ 703 is listed at 0.86 at 250 Hz and 1.14 at 500 Hz, while the model gives about 0.3 and 0.65. Real panels in a room behave somewhere between the two.
Membrane absorbers: f₀ = (1/2π)·√(γP₀/(m·D)) ≈ 60/√(m·D) with an empty cavity, or ≈ 50/√(m·D) with fill (the air spring becomes isothermal). m is in kg/m² and D in m. The full curve treats the sheet as a limp mass with a loss factor in front of a locally reacting cavity. The bending stiffness of the panel is ignored, so thin, stiff and small panels resonate higher than the formula.
Helmholtz panels: f₀ = (c/2π)·√(ε/(D·t′)), where ε is the open-area fraction and t′ = t + δ. For round holes δ = 0.85·d·(1 − 1.14√ε) (Ingard’s end correction with the hole-interaction factor in Allard & Atalla). For slots δ = (2w/π)·ln(1/sin(πε/2)) (Smits & Kosten, Vigran). The curve adds Ingard’s viscous resistance and the fill.
Diffusers follow Schroeder and Cox & D’Antonio (Acoustic Absorbers and Diffusers). The scattering is a Fraunhofer (Kirchhoff) far-field sum over the wells, each with reflection factor e^−2jkd. That is good for the shape of the lobes and their trends, but not for absolute levels near grazing. The diffusion coefficient follows AES-4id: d = ((ΣI)² − ΣI²)/((n − 1)·ΣI²), 37 receivers, normalised against a flat panel of the same width.
RT60 uses the functions of the acoustics tool directly, so the two agree: Sabine T = 0.161·V/A and Eyring T = 0.161·V/(−S·ln(1 − ᾱ)). The targets are EBU Tech 3276 for control rooms (Tm = 0.25·(V/100 m³)^⅓ s ± 0.05 s, with more allowed in the bass), IEC 60268-13 for listening rooms (0.3–0.6 s), and ANSI/ASA S12.60 for classrooms (≤ 0.6 s). The home theatre, live room and booth ranges are common practice.
Transmission loss. Below fc/2 a single leaf follows the field-incidence mass law 20·log₁₀(m·f) − 47 dB. Above the critical frequency fc = (c²/2π)·√(m/B) it follows Cremer’s resonant transmission 20·log₁₀(m·f) − 42.4 + 10·log₁₀(2ηf/(π·fc)), with the loss factor η plus EN 12354-1 boundary losses. Between the two the line is straight on a log-frequency scale. Screwed layers add their masses and bending stiffnesses, so two sheets keep the fc of one. Double walls follow Sharp (1978): the mass law of the total mass below the mass–air–mass resonance f₀, then R₁ + R₂ + 20·log₁₀(f·d) − 29, then R₁ + R₂ − 6 above c/(2πd). That result is capped by Sharp’s line-bridge (studs) or point-bridge (resilient channel) path. The extra decoupling of steel studs, staggered studs and channel is an empirical allowance chosen to land near published results. Green Glue is modelled only as damping (η ≈ 0.15 in that leaf). An empty cavity costs 6 dB.
Ratings. STC follows ASTM E413: the highest contour with at most 32 dB of total deficiency and no band more than 8 dB below it, 125 Hz–4 kHz. Rw follows ISO 717-1: the reference curve shifted in 1 dB steps until the unfavourable deviations reach 32.0 dB, 100 Hz–3.15 kHz, with C and Ctr from the pink-noise and traffic spectra.
Published comparisons are typical laboratory values from NRC Canada (IR-761 and IR-693), Gypsum Association GA-600 and glass makers' data. The table shows the model’s error for each. It is usually within 3–5 points, and worst for shared wood studs (over) and wide double-stud cavities (under).

These are estimates for comparing options. Real walls lose 5–10 points in the field through flanking paths — doors, outlets, ducts, gaps, continuous floors and ceilings. Real absorbers depend on how they are mounted. Measure before promising anyone a result.

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Method and assumptions

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