What is the sound reduction index R_w

The sound reduction index R_w (w = weighted) of a wall is its capacity to reduce the sound level transmitted from one room to another. Measured in decibels (dB), it is the difference between the source room's sound level and the receiving room's, weighted with a standard reference curve (ISO 717-1). R_w = 50 dB means the wall attenuates transmitted noise by 50 dB: 80 dB in one room → 30 dB in the adjacent one (near silence). Italian regulation DPCM 5/12/1997 requires R'_w ≥ 50 dB between residential units; UNI 11367 (2010) introduces 4 acoustic classes (I-IV). Design calculation uses the mass law (Berger 1920) or FE software (INSUL, SONarchitect).

The mass law (Berger 1920): R_w = 20·log₁₀(m·f) − 47.4

The mass law is the fundamental relation: the heavier the wall, the better it insulates against airborne noise. Formalised by Rudolf Berger in 1920 for single homogeneous walls:

R(f) = 20·log₁₀(m · f) − 47.4  [dB, single frequency]

with m wall surface mass (kg/m²) and f frequency (Hz). Weighted R_w is approximated at f = 500 Hz (mean speech-band frequency):

R_w ≈ 20·log₁₀(m·500) − 47.4 = 20·log₁₀(m) + 6.6  [dB]

Example: solid brick wall with plaster, mass 200 kg/m² (~15 cm) → R_w = 52.6 dB. Doubling mass adds 6 dB (log doubling), tenfold adds 20 dB. Slow relation: to go from R_w = 40 to 50 dB (10× sound reduction) requires doubling mass.

Performance jump: double wall with mineral-wool cavity

The mass law says reaching R_w = 60 dB with a single wall requires ~800 kg/m² (45 cm concrete). Double wall with cavity exploits the mass-spring-mass effect for the same performance with much less mass. Principle: two rigid masses (the two walls) connected by a "spring" formed by air, acting as oscillator. Above resonance frequency, wall-cavity-wall pair mechanically decouples vibrations. Optimised by adding fibrous material (mineral wool, glass wool, polyester) in the cavity, dissipating sound energy by viscous friction without adding stiffness. Typical bonuses:

• 50 mm empty air cavity: +3 dB vs equivalent single wall.
• 50 mm cavity with 40 mm mineral wool: +10 dB.
• 100 mm cavity with 80 mm mineral wool: +14 dB.
• Double metal stud with double board and wool: +18-20 dB.

Example: double 2×12.5 mm plasterboard on 75 mm metal studs with 60 mm rock wool. Total mass 25 kg/m². R_w calculated: 41.9 + 12 = 53.9 dB. Solid 200 kg/m² masonry gives 52.6 dB — the lightweight wall matches with 8× less mass!

Critical frequency and coincidence: the insulation dip

Mass law is valid mid-spectrum (100-2000 Hz). At high frequencies a critical phenomenon appears: coincidence (coincidence dip). Every rigid panel has a critical frequency f_c where sound wavelength in air matches the panel's bending wavelength. At f_c insulation drops 10-20 dB (spectral hole). Typical panels:

• 15 cm concrete: f_c ≈ 130 Hz (low, low speech impact).
• 12.5 mm plasterboard: f_c ≈ 3200 Hz (high, big speech problem).
• 4 mm glass: f_c ≈ 3000 Hz.
• 10 mm glass: f_c ≈ 1200 Hz.

Countermeasures: plates of different mass/thickness (different critical frequencies); viscoelastic damping layers (ISOCOM between two boards); double boards with vacuum. Mass law calculation does NOT account for coincidence — for light panels with high f_c it may overestimate R_w by 5-15 dB.

Acoustic classification (UNI 11367)

UNI 11367:2010 (Italian building acoustic classification) has 4 classes:

• Class I (excellent): R'_w ≥ 56 dB, L'_nw ≤ 53 dB, D_2m,nT,w ≥ 43 dB. Luxury, hospitals, high-standard schools.
• Class II (good): R'_w ≥ 53 dB, L'_nw ≤ 58 dB, D_2m,nT,w ≥ 40 dB. Quality residential.
• Class III (basic): R'_w ≥ 50 dB, L'_nw ≤ 63 dB, D_2m,nT,w ≥ 37 dB. Minimum legal requirement DPCM 5/12/1997.
• Class IV (insufficient): below Class III. Non-compliant in Italy.

Main parameters: R'_w apparent airborne sound insulation of vertical partitions; L'_nw impact sound pressure level (floors); D_2m,nT,w façade insulation (outdoor noise). UNI 11367 requires on-site certification via measurements per UNI EN ISO 16283-1/2/3.

Typical materials and layers

• Single 12.5 mm plasterboard: mass 10 kg/m², R_w = 26 dB.
• Double 2×12.5 mm plasterboard on 50 mm studs + 40 mm mineral wool: R_w = 48 dB (non-compliant Class III).
• Double 2×12.5 mm plasterboard on 75 mm studs + 60 mm mineral wool: R_w = 54 dB (Class II).
• Triple 3×12.5 mm plasterboard on 100 mm studs + double wool: R_w = 60 dB (Class I).
• 8 cm hollow brick + 1.5 cm plaster both sides (m=130): R_w = 41 dB (non-compliant).
• 12 cm solid brick + plaster (m=220): R_w = 46 dB (non-compliant Class III).
• Double hollow brick 8+8 cm with 40 mm wool in cavity (m=270): R_w = 53 dB (Class II).
• 20 cm concrete block (m=450): R_w = 55 dB (Class II).

Flanking losses and R_w vs R'_w difference

R_w is measured in lab with wall perfectly isolated from flanking (adjacent structures). On-site sound also transmits through side structures (floors, perpendicular walls, acoustic bridges) — flanking transmissions. Real on-site R'_w is always less than R_w:

• Traditional brick construction: R'_w = R_w − 3-4 dB.
• RC construction with continuous floors: R'_w = R_w − 5-8 dB (vibrations run along floors).
• Well-decoupled lightweight walls: R'_w = R_w − 1-2 dB.

To meet code on-site, design R_w 5-8 dB above legal limit: for R'_w ≥ 50 dB need R_w ≥ 55-58 dB in lab. Flanking controlled by: perimeter elastic joints, wall-floor decoupling (mineral wool or rubber strips), interruption of acoustic bridges (spring hangers on metal studs), pipe insulation.

How to use the calculator

Enter first wall surface mass m1 in kg/m². For single wall, leave wall 2 mass = 0; for double wall enter second layer mass. Solid brick 12 cm + double plaster: m ≈ 220-260 kg/m². Plasterboard 12.5 mm: m ≈ 10. Solid concrete 20 cm: m = 500. Consult manufacturer sheets or CNR 10011 tables. If double wall: enter cavity thickness in mm (5-100 typical) and fibrous insulation thickness in mm (30-100 typical). Choose cavity fill type: 1 = mineral wool / acoustic polyester; 2 = only air. Calculator returns total mass, R_w of wall 1 only, R_w of wall 2 (0 if absent), total lab R_w, on-site R'_w (with flanking losses ~-3 dB), predicted residual noise in receiving room for 80 dB source, and assessment with UNI 11367 acoustic class and DPCM 5/12/1997 compliance.