Understanding the Sabin's Formula
Developed by Wallace Clement Sabine, the "father of architectural acoustics," the Sabin's formula is used to calculate the reverberation time of a room. Reverberation time (T60) is the time it takes for sound to decay by 60 decibels after the sound source stops. The formula connects a room's volume, surface area, and the sound absorption of its materials.
The standard metric formula is:
$T = 0.161 \frac{V}{A}$
Here:
- T is reverberation time in seconds.
- V is the room's volume in $m^3$.
- A is total sound absorption in metric sabins ($m^2$).
- 0.161 is a constant for metric units (0.049 for imperial).
Calculating Total Sound Absorption (A)
The total sound absorption (A) is the sum of the absorption contributions from all surfaces and objects in the space. It's calculated as:
$A = \sum (S_i \cdot \alpha_i)$
Where:
- $S_i$ is the surface area of a material in $m^2$.
- $α_i$ is the material's sound absorption coefficient (0 to 1).
Absorption coefficients for various materials and objects can be found in reference tables for different frequencies.
The Unit of 'Sabin'
Total absorption is often measured in 'sabins.' One sabin is equivalent to the absorption of one square meter (or square foot) of a perfectly absorptive material, honoring Wallace Sabine.
Limitations and Alternatives
The Sabin's formula assumes a diffuse sound field and is less accurate in rooms with complex shapes, non-uniform absorption, or high absorption levels. It also doesn't inherently account for frequency dependence of absorption or air absorption in large spaces, though corrections can be added. For highly absorptive rooms, the Eyring formula offers greater accuracy.
Comparison: Sabine vs. Eyring Formula
| Feature | Sabine Formula | Eyring Formula |
|---|---|---|
| Application | Suitable for acoustically "live" rooms (low absorption). | More accurate for acoustically "dead" rooms (high absorption). |
| Mathematical basis | Empirical, based on Sabine's observations. | Theoretical, derived from wave theory principles. |
| Absorption range | Less accurate for total absorption values greater than 0.2. | Remains accurate even with high absorption values. |
| Predictive accuracy | Can predict absorption coefficients greater than 1.0 in some cases. | Predicts accurate absorption coefficients between 0 and 1. |
| Underlying assumption | Assumes a perfectly diffuse sound field. | Assumes a non-diffuse, less idealized sound field. |
Not All Sabin is Acoustics: The Virology Connection
The name "Sabin" is also associated with Albert Sabin, the virologist who developed the oral polio vaccine. This is unrelated to the acoustic formula and context is important to avoid confusion.
Practical Application
The Sabin's formula is a fundamental tool for initial acoustic design. It helps estimate reverberation time and determine the amount of sound-absorbing material needed. The process involves setting goals for reverberation time, measuring room properties, calculating initial time, modeling the effect of adding absorptive materials, and refining the design. For complex projects, more advanced formulas or modeling may be used.
In summary, the Sabin's formula is a simple, foundational method in architectural acoustics for understanding the relationship between a room's physical characteristics and its sound decay, guiding the process of creating acoustically functional spaces.
For more detailed information, consult the ScienceDirect overview of the Sabine equation.
