Mass stops sound
Sound that hits a wall makes it vibrate, and the vibrating wall radiates sound on the other side. The heavier the wall, the less it moves, and the less sound gets through. This is the mass law: for a single, uniform wall, the insulation rises by about 6 dB each time the mass per square meter doubles, and by about 6 dB for each doubling of frequency. Bass is therefore always harder to block than treble.
The formulas
- Surface mass: m = density × thickness, in kg/m²
- Mass law (field incidence): R ≈ 20 log₁₀(m × f) − 47 dB, with f in Hz
- Rw estimate for heavy walls: Rw ≈ 37.5 log₁₀(m) − 42 dB, for m ≥ 150 kg/m²
Rw, from ISO 717-1, is close to the STC rating used in North America (ASTM E413); the two usually agree within a few decibels.
Example: a 6-inch concrete wall
- Surface mass: 2,300 kg/m³ × 0.1524 m = 350.5 kg/m² (71.8 lb/ft²)
- At 500 Hz: 20 log₁₀(350.5 × 500) − 47 = 58 dB
- At 125 Hz: 46 dB; at 2,000 Hz: 70 dB
- Rw ≈ 37.5 × log₁₀(350.5) − 42 = 53 dB
A single sheet of 1/2-inch gypsum board, about 9 kg/m², gives only about 26 dB at 500 Hz by the mass law.
Reading the result
- A loud voice is about 70 dB. With 50 dB of insulation it arrives at 20 dB, barely audible in a quiet room.
- Doubling a concrete wall’s thickness adds only about 6 dB at a given frequency, at the cost of twice the weight.
- Light walls reach high ratings with double construction: two leaves on separate studs, an air gap and absorbent insulation. The mass law of a single leaf underestimates them in the middle frequencies.
Limits
Real walls fall short of the mass law near the coincidence frequency, where bending waves in the panel match the wavelength of sound in air. For thick concrete this happens around 100 Hz; for glass and drywall it lies between about 1,000 and 3,000 Hz. Results in a building are lower still because of flanking through floors, ceilings and junctions, and because of leaks around doors, outlets and ducts. Use this calculator for first estimates and comparisons, not for compliance.