Acoustics
Mass law sound reduction of a single leaf
- where
- sound reduction (dB)
- surface mass of the leaf (kg/m²)
- frequency (Hz)
- incidence constant, 47 field or 48 random (dB)
Explain this equation
Estimates how much a single solid leaf, such as one or more boards fixed together, reduces airborne sound at one frequency.
m is the surface mass in kg per m², from the board data sheets; f is the frequency in hertz. The product m·f stands for how hard it is for the sound pressure to shake the leaf: heavier leaves and higher frequencies both resist more. K is a constant that sets the units and the angle of incidence: 47 for sound arriving from a typical spread of angles, 48 in some texts for fully random incidence.
The leaf behaves as a mass resisting the pressure, so the transmitted sound falls with the square of m·f, which on a decibel scale is 20 log, or 6 dB for each doubling.
Sense check: a 10 kg/m² board at 500 Hz gives about 27 dB; double the mass and it gives about 33 dB.
Watch out: stud walls with two leaves and insulation beat the mass law; use tested Rw values for compliance, and the law fails near the coincidence frequency.
Estimates the airborne sound reduction of a single solid leaf (one or more boards fixed together) from its weight per m², at one frequency.
Enter your values to see the result.
Good to know
The mass law says a limp, single leaf gains about 6 dB for every doubling of its surface mass or of frequency. With m in kg/m² and f in Hz the field-incidence form is R ≈ 20 log(m·f) − 47 dB (normal incidence − 42 dB, less about 5 dB for sound arriving from many angles); some texts use − 48 for random incidence. Board surface masses are on the data sheets (about 8–14 kg/m² for 12.5–15 mm boards).
Common mistake
Using the mass law to predict a stud partition. Two leaves on a frame with insulation in the cavity perform far better than the mass law for their combined weight; use the manufacturer's tested Rw.
Limits
Single leaf only, below the coincidence frequency (for plasterboard, roughly 2.5–3 kHz for 12.5 mm). It is a physics estimate at one frequency, not an Rw rating; flanking, air gaps and junctions usually dominate on site. Use tested values for Building Regulations Approved Document E.
Sources
- D. W. Herrin, University of Kentucky Vibro-Acoustics Consortium, Empirical models: normal-incidence mass law TL = 20 log(ρs·f) − 42 dB; field incidence TL = normal − 5 dB
- NRC Canada, Canadian Building Digest CBD-239: Sound transmission through walls (TL = 20 log(m·f) − 48, m in kg/m², f in Hz; +6 dB per doubling of mass or frequency; coincidence dips)
- K. Ballagh, Accuracy of prediction methods for sound transmission loss, NZ Acoustics 2003 (single panel R = 20 log(m·f) − 48)
Results are calculations from the published methods and manufacturer figures shown, and depend on the data you enter. Always follow the manufacturers’ system and product data, BS 8212, BS EN 13914 and Building Regulations. Coverage rates vary by product, background and thickness. Check prices, VAT and CIS rules with your own records and HMRC.