Mass Law Transmission Loss

For a single limp panel, blocking airborne sound is a question of inertia. The sound field pushes on the panel; the panel's mass resists being accelerated; the heavier it is, and the faster the pressure alternates, the less it moves and the less it radiates on the far side. Working that through gives transmission loss as $20\log_{10}(\pi m f/\rho_0 c)$, where $m$ is surface density in kg/m² and $\rho_0 c \approx 415$ rayl is the characteristic impedance of air. Because it is a 20-log law, doubling the mass adds 6 dB, and doubling the frequency adds 6 dB.

Real buildings use the field-incidence version, about 5 dB below the normal-incidence result, because sound in a room arrives from every direction rather than square-on. Fold the constants together and the practical form appears: $TL = 20\log_{10}(m f) - 47.4$ with $m$ in kg/m² and $f$ in hertz. Convert to pounds per square foot and the same law reads $TL = 20\log_{10}(m f) - 33.5$, because one lb/ft² is 4.882 kg/m² and $20\log_{10}(4.882) = 13.8$ dB of the constant moves across. Two handbooks quoting "the mass law" with different constants are quoting the same physics in different units — this calculator pins the surface density to kg/m² and applies the metric form.

Treat the answer as a ceiling. Real panels are stiff, and stiffness introduces the coincidence effect: at the frequency where the panel's bending wavelength matches the wavelength of sound in air at grazing incidence, the panel couples efficiently to the air and its transmission loss collapses into a dip of 10 dB or more. Thin and stiff is the worst combination, which is why the dip for 13 mm gypsum board lands near 2.5 kHz and for window glass squarely in the speech range. Below the panel's fundamental resonance the mass law does not apply either.

The deeper limitation is that the law describes ONE leaf, and the 6 dB per doubling is a brutal economics: 10 dB more isolation needs roughly triple the mass, 20 dB needs ten times. That road runs out quickly, and it is why practical isolation goes to two leaves with a cavity between them — a mass-spring-mass system that can far exceed the mass law well above its own resonance, provided the two leaves are not connected. Connect them with a rigid tie and the assembly reverts to the mass law with a poor coincidence dip, which is what a stud bridging both faces does and what resilient channels, staggered studs and separate frames exist to prevent.