Sound Transmission Loss Formula
Calculate how much sound a wall or barrier blocks using the mass law TL = 20 log(f m) - 47.
Essential for soundproofing and building design.
The Formula
The Sound Transmission Loss formula, often called the mass law, predicts how many decibels of sound a solid barrier will block. It was first described systematically in the early 20th century as engineers began studying noise control for factories and urban buildings. The idea is straightforward: heavier walls block more sound, and higher-frequency sounds are easier to block than low-frequency sounds. The formula shows that every time you double either the wall mass or the sound frequency, transmission loss increases by about 6 dB. Since 6 dB represents a halving of perceived loudness, this is a significant improvement. This is why bass frequencies from music or traffic rumble are so difficult to block. A wall that effectively stops mid and high-frequency speech can still let deep bass pass through almost unimpeded.
The mass law is a simplified model that assumes an infinite, limp panel with no structural stiffness. Real walls have resonance frequencies where transmission loss drops sharply, and they have a coincidence frequency where bending waves in the panel match the sound wavelength, creating another dip in performance. Despite these limitations, the mass law provides an excellent starting point for soundproofing design. Building codes and acoustic consultants use it to estimate the Sound Transmission Class (STC) rating of wall assemblies. For residential construction, a single layer of 16 mm (5/8 inch) drywall on each side of a stud wall gives roughly STC 33, while doubling the drywall on one side bumps it to about STC 38. Adding insulation in the cavity and using resilient channels can push performance well above what the simple mass law predicts, because these strategies break the structural path that sound vibrations travel through. The mass law formula remains the foundation upon which all these more advanced techniques are evaluated.
Variables
| Symbol | Meaning |
|---|---|
| TL | Transmission loss (dB) — how much quieter the sound is on the other side |
| f | Sound frequency (Hz) |
| m | Surface mass density of the barrier (kg/m²) |
| 47 | Constant for SI units (use 33 for imperial units with lb/ft²) |
Example 1: Concrete Wall at Speech Frequency
A 150 mm (6 in) concrete wall has a surface density of 350 kg/m². How much does it reduce a 1,000 Hz sound?
TL = 20 × log10(f × m) − 47
TL = 20 × log10(1000 × 350) − 47
TL = 20 × log10(350,000) − 47
TL = 20 × 5.544 − 47
TL ≈ 63.9 dB reduction (excellent isolation for speech frequencies)
Example 2: Single Drywall Sheet at Low Frequency
A standard 12.5 mm (1/2 in) drywall sheet has a surface density of about 10 kg/m². What is the transmission loss at 125 Hz (bass guitar range)?
TL = 20 × log10(f × m) − 47
TL = 20 × log10(125 × 10) − 47
TL = 20 × log10(1250) − 47
TL = 20 × 3.097 − 47
TL ≈ 14.9 dB (poor isolation — bass easily passes through thin drywall)
When to Use It
Use the mass law whenever you need a quick estimate of how much sound a barrier will block.
- Designing soundproof walls for home studios and practice rooms
- Estimating noise reduction for office partition walls
- Comparing wall construction options for residential buildings
- Highway noise barrier design and environmental noise control
- Industrial enclosures for loud machinery
- Evaluating window glass thickness for noise-sensitive buildings