Decibel

Overview

Decibel weighting filters adjust sound pressure measurements to match human hearing perception, which is most sensitive in the 1–4 kHz range. The A-weighted filter (dB(A)) is the most common standard for environmental and occupational noise assessment. B and C weighting filters are less frequently used today but provide alternatives for different sound pressure levels and frequencies.

Key Formulas

Logarithmic Combination of Sound Levels

$$L_{total} = 10 \cdot \log_{10}\left(10^{L_1/10} + 10^{L_2/10}\right)$$

Formula for combining two decibel levels logarithmically. The same principle extends to multiple sources.

Sound Intensity Level

$$L = 10 \log_{10}(I/I_0)$$

Where $I_0$ is the reference sound intensity (typically $10^{-12}$ W/m²).

Variables

Decibel Filter Weighting

Sound level meters apply frequency-dependent weighting filters to approximate human hearing response. The dB(A) filter approximates the 40-phon equal-loudness contour. dB(C) is nearly linear for high sound pressure levels, while dB(B) falls between them and is rarely used in modern practice. The abbreviation "dB(A)" is common engineering shorthand, though SI recommends phrasing like "the A-weighted sound pressure level is x dB."

Frequency Response Data

Example: A-Weighted Level Calculation

To find the total dB(A) from octave band measurements, apply the filter correction to each band, then combine logarithmically. Below is a sample calculation:

To combine the resulting levels logarithmically, pair the highest values and use the combination formula repeatedly. Starting with the two highest bands (250 Hz and 500 Hz):

1. Difference: 55 - 49 = 6 dB → Add 1 dB to the higher value: 55 + 1 = 56 dB(A)
2. Add next highest (1000 Hz): Difference: 56 - 48 = 8 dB → Add 0.5 dB: 56 + 0.5 = 56.5 dB(A)
3. Remaining levels are significantly lower. The total estimated level is ~56.5 dB(A).

A, B and C Weighted Sound Level Calculator

The original page includes spreadsheet-style dB(A), dB(B) and dB(C) calculations. Enter octave-band sound pressure levels below; the calculator applies the weighting corrections and combines the bands logarithmically.

dB(A) Level Adjustment Guidelines

A baseline criterion of 40 dB(A) is commonly adjusted for time, location, and sound character.

Restored Original Source Tables

The following tables are restored from the original source page to preserve the complete reference data.

Decibel A, B and C

Decibel A Filter

Decibel A - Adjustments to Context

Engineering Notes

• The A-weighting filter underestimates low-frequency noise, which can be significant for complaints about HVAC systems, transformers, or traffic rumble.
• C-weighting is often used for peak sound pressure measurements or where low-frequency content is important, such as assessing blast or impact noise.
• When combining levels logarithmically, adding a sound source that is 10 dB lower than the existing level contributes only 0.4 dB to the total—sources 10+ dB below the dominant level are often negligible.
• Regulatory limits typically use dB(A) for environmental noise, but specific applications (e.g., military, industrial) may use other metrics like dB(C) or unweighted dB.
• The SI unit for sound level is the decibel (dB), but it is dimensionless. Always specify the weighting filter (A, B, or C) when reporting.

References

Original Source: engineeringtoolbox.com