Wall Sound Insulation Calculator: Mass Law, Double Walls & Leaks

Surface mass is calculated as $m=\rho_{leaf}t$, using the effective density and summed material thickness of each leaf. Density and thickness convert with the metric/US switch; frequency is unchanged. The schematic and sensitivity chart explicitly retain SI labels.

Single leaf

Use SI numerical values in Sharp's field-incidence mass law, $R_M=20\log_{10}(\pi fm/Z_0)-5$, with $Z_0=411.6$ Pa·s/m. Below $f_c/2$, this is the leaf estimate. At and above coincidence use $R_c=20\log_{10}(\pi fm/Z_0)+10\log_{10}(2\eta f/(\pi f_c))$. Interpolate in dB against log frequency between the two endpoints at $f_c/2$ and $f_c$. Clip TL to zero to preserve passivity. See the attached AAS 2015 paper, PDF p.3, Eqs.4 and 6. The printed sign in Ballagh's Eq.2 is inconsistent with damping physics; this calculator uses the positive damping contribution in the AAS equation: more damping raises coincidence TL.

Separated double leaf

Air stiffness per area is $K_a=\rho_0c_0^2/d$, and $f_0=\sqrt{K_a(1/m_1+1/m_2)}/(2\pi)$. Sharp's absorbent-cavity asymptotes are $R_1+R_2+20\log_{10}(fd)-29$ below the cavity transition and $R_1+R_2+6$ above it; the transition is approximately $55/d$ Hz. These are the equations reproduced and experimentally assessed by Ballagh (2004), PDF p.2. Critical-frequency effects are included in both leaf terms.

Sharp's asymptotes do not resolve the resonance dip. Here a derived extension, not Sharp's original model, supplies it. For each frequency form $z_j=i\omega m_j$ and $Y=i\omega d/[\rho_0c_0^2(1+i\eta_a)]$. Multiplication of the series-mass, shunt-compliance and series-mass transfer matrices gives the loaded pressure denominator

Use $\max(0,20\log_{10}|D/2|-5)$ below $f_0$. The subtraction of 5 dB is an approximate field correction. Between $f_0$ and $2f_0$, blend its transmitted power into the Sharp estimate using $u=\log_2(f/f_0)$ and $w=u^2(3-2u)$; use Sharp alone above $2f_0$. This numerical transition and the default cavity damping are screening assumptions. Inputs that overlap the resonance, cavity-transition or coincidence regimes are rejected.

Openings, bands and ratings

For open fraction $a=A_{open}/A$, $R=-10\log_{10}[(1-a)10^{-R_{wall}/10}+a]$. This follows conservation of transmitted power; ASHRAE 2025 Fundamentals, Ch.8 Eq.41. The opening-only ceiling is $-10\log_{10}a$. Nine log-frequency midpoint samples approximate each third-octave band's mean transmitted power, assuming equal incident energy per logarithmic frequency interval.

Before fitting, round the band values within the shared rating function: to the nearest integer dB for STC (ASTM E413-22 §5.2), and to the nearest 0.1 dB for Rw (ISO 717-1:2020 §4.4, printed p.4 / attached preview p.10). Accumulate deficits in integer dB or integer tenths of a dB so numerical roundoff cannot alter the 32 dB limit. This rounding applies to modeled and measured band inputs, not only their displayed precision.

Fit the highest integer contour: ASTM E413-22 STC uses 125–4000 Hz, a total deficit no greater than 32 dB and an individual deficit no greater than 8 dB. ISO 717-1:2020 Rw uses 100–3150 Hz and the 32 dB total rule. Both are evaluated at 500 Hz. Functional contour descriptions implement the method without reproducing standard tables or figures. These are estimates from modeled bands, not standard-compliant measurements; check against the standard in force.

• Fixed air properties: density 1.2 kg/m³ and sound speed 343 m/s, representative of room-temperature air. Empirical function arguments are normalized to Hz, kg/m² and metres before evaluation.
• Broad, thin, effectively homogeneous leaves. Surface mass and effective critical frequency are independent user data; no automatic stiffness model for bonded laminates or multilayer boards is assumed.
• Double leaves have separate supports, fibrous cavity absorption, sealed perimeters except the entered opening, and no structural bridges or flanking paths. Absorber flow resistivity and fill distribution are not modeled.
• The default 800 kg/m³ and 12.5 mm per leaf give 10 kg/m². This matches the surface masses in NRC TL-93-279; the 205 mm cavity also follows that test. The default density/thickness pair is an illustrative way to enter the mass, not a material specification. The 3000 Hz critical frequency, 0.03 leaf loss and 0.15 air-spring loss are illustrative assumptions, not measured properties of that specimen.
• The lumped resonance extension and power interpolation are derived here. The dip's depth is particularly uncertain. This is a static frequency-domain sizing tool; no animation is needed.

Use for preliminary comparisons over 50–5000 Hz with the stated separated-leaf assumptions. The band calculations extend slightly past the plotted limits to integrate the end bands. This is an estimate, not a lab rating.

NRC IR-761 provides independent checks, not fitted coefficients. For TL-93-279 (printed p.316, attached PDF p.319), the default sealed model gives STC 52 versus measured 53, and about 59.1 dB at the 500 Hz band versus 60.0 dB measured. Across 125–2000 Hz the largest band discrepancy is approximately 3 dB. Across the complete plotted range, error approaches 14 dB near resonance, and approximately 9 dB near coincidence. The fixed comparison chart shows these differences. For TL-93-262 (printed p.330, PDF p.333), 11.6/11.4 kg/m² leaves and 205 mm depth give approximately STC 54 versus measured 58 using an assumed 2500 Hz critical frequency. Reference-case tolerances of 3–5 dB are limited screening checks at specified points; they are not a universal accuracy claim.

No prediction of room-to-room level difference, reverberation, flanking, shared studs, resilient mounts, empty cavities, absorber-product performance, slit diffraction, duct resonances, triple leaves, heavy masonry shear waves or fire resistance. Do not use the open-area model as a ventilation or narrow-crack acoustic design method.

STC/Rw fitting follows ASTM E413-22 and ISO 717-1:2020 respectively; standards and scope checked on 29 October 2026. Obtain measured assembly ratings for specifications and check against the standard in force. Installation work belongs to a qualified person.