Sound Source: How SLC80 Is Calculated

*When I compare the values in the attenuation charts with the SLC*_{80}* on the package, the SLC*_{80}* is much lower than the average attenuation. How is the SLC*_{80}* calculated?*

It is quite an ambitious calculation to measure a hearing protector’s attenuation at a variety of frequencies on a few test subjects in the laboratory, input these values into a formula and derive a single-number rating that can be applied universally to all users in all noise settings. If you have studied the attenuation charts on boxes of hearing protectors, you can see the Sound Level Conversion (SLC_{80}) is not simply a mathematical average of the attenuation values*. Here are the significant steps used in calculating the SLC_{80}, and an explanation of why each step is important:

**Laboratory Testing**

Inexperienced test subjects with normal hearing are selected at random (sixteen subjects are used for testing earmuffs, twenty subjects for earplugs). Subjects are tested with hearing protectors (called occluded ear), and tested again without hearing protectors (called open ear), across a range of test frequencies. The difference between the open ear and occluded hearing tests gives us the attenuation of the hearing protector. The variability in these attenuation measurements among subjects (the “Standard Deviation”) is calculated and the attenuation values from all subjects are then averaged to give us the “Mean Attenuation in dB” at each frequency. These Mean Attenuation values, as well as the Standard Deviations, appear in the attenuation chart on each box or bulk package of hearing protectors.

**Subtract Standard Deviation**

To account for individual variation in fitting hearing protectors out in the real world (remember, the laboratory only tested twenty subjects, at most), a correction factor of one standard deviation is subtracted from each attenuation value. By subtracting one standard deviation, we can generalize the results from a small sample of twenty subjects to a larger population: for a population which is properly fitted with the HPD in the same manner as the laboratory subjects, 80% of the population would be expected to achieve these same attenuation values.

**Subtraction from Hypothetical Noise**

To account for some differences between the laboratory test sounds and real-world noise, the adjusted attenuation values (mean minus one standard deviation) are subtracted from “hypothetical noise levels” – some standardized noise levels at each frequency band. This step is critical in making the SLC_{80 }more relevant to a hearing protector user, and not a laboratory microphone which detects sound differently than a human ear.

**Logarithmic Addition**

Finally, we combine all the adjusted attenuated levels into a single number. Attenuation values are measured in decibels, which are logarithmic numbers. (From math class, you may recall logarithms are related to the exponent of a number, or the power to which a number is raised.) Logarithms cannot just be added mathematically (80 dB plus 80 dB does not equal 160 dB). They are added in a special way that accounts for the exponents, and the result is then subtracted from 100 (the logarithmic sum of the hypothetical noise levels).

The result of this lengthy calculation is the SLC80 – a single-number rating of a hearing protector’s attenuation. The SLC_{80} is significantly lower than the average attenuation across all frequencies because the SLC_{80} contains corrections and cushions to make it applicable to a broader population. While it is not a perfect real-world measure of attenuation, the SLC_{80} is a very useful standardized method for describing a hearing protector’s attenuation in a single number. It estimates the amount of attenuation provided to at least 80% of users in a variety of noise environments, when the protector is properly fitted.

To determine the class of a hearing protector, the SLC_{80} is applied to Table 2. Included in this class determination is an additional adjustment to correct for varying noise spectra in typical workplaces. This means that a Class 4 hearing protector, for example, can be effectively used in a 102 dB noise, across a broad range of noise sources and workplaces.

Footnote:

* Calculation of the SLC_{80} is defined in Australian/New Zealand Standard 1270:2002, “Acoustics – Hearing Protectors