RB-03Room & Building Acoustics

Panel Transmission Loss

Mass law, coincidence frequency and a sound reduction index estimate for single-leaf panels.

Panel

Material

Thickness

E = 2.5 GPaρ = 800 kg/m³ν = 0.3η = 0.02

Surface mass m''

10kg/m²

Critical frequency

2,800Hz

R at 500 Hz

27.0dB

Mean 100–3150 Hz

25.0dB

Sound reduction index

Estimated R (Sharp)Mass law

Panel section & bending wave

§ Theory of operation

The mass law

Below its resonances and coincidence, a single-leaf panel resists sound purely by its inertia. The heavier the panel and the higher the frequency, the less it moves. For a diffuse (field-incidence) sound field:

R \approx 20\,\log_{10}(\,m''{\cdot}f\,) - 47 \quad \mathrm{dB} \qquad (m''\ \mathrm{in\ kg/m^2})

Each doubling of mass or of frequency adds about 6 dB. (For normal incidence the constant is −42.) In practice measured values follow the mass law with a slope closer to 5 dB per doubling.

The coincidence dip

Bending waves in a plate are dispersive, their speed increases with $\sqrt{f}$ . At the critical (coincidence) frequencythe bending wavelength matches the trace wavelength of sound in air at grazing incidence, the panel couples efficiently to the air and transmission increases dramatically:

f_c = \dfrac{c^2}{2\pi}\,\sqrt{m''\,/\,B} \qquad B = E\,h^3\,/\,12(1 - \nu^2)

Above $f_c$ , the depth of the dip and the recovery depend on the loss factor η. This tool uses Sharp's method:

\begin{aligned} f < f_c/2&:\quad R = 20\,\log_{10}(m''{\cdot}f) - 47 \\ f \ge f_c&:\quad R = 20\,\log_{10}(m''{\cdot}f) + 10\,\log_{10}(2\eta f\,/\,\pi f_c) - 47 \\ \text{between}&:\quad \text{straight line on a log-frequency axis} \end{aligned}

Design implications

Stiff, light materials (glass, plywood, steel) have coincidence in the speech range - a weakness exploited by laminated glass and damped panels.
Thick masonry has $f_c$ below 200 Hz, so it behaves well across the speech range.
Thin, limp, heavy materials (lead, mass-loaded vinyl) push $f_c$ above audibility and follow the mass law throughout.
Doubling a single leaf adds only ~5 dB; decoupled double-leaf constructions with absorbent infill do far better.

Results are estimates for infinite, unbridged panels. Real walls are limited by flanking, gaps and edge conditions.