Sound level composition

How do you use the tool?

The tool covers three cases: summing the contributions of several sources operating simultaneously to obtain the total level at the receiver; computing the overall level from frequency bands measured separately (e.g. the 63 Hz – 8 kHz octaves); and subtracting background noise from a measurement to isolate the source of interest. The sum is energetic, not arithmetic.

Three typical cases:

1. Summing the contributions of several sources operating simultaneously (e.g. fan + compressor + traffic) to obtain the total level at the receiver.
2. Computing the overall level from frequency bands measured separately (e.g. summing the 63 Hz – 8 kHz octaves).
3. Subtracting background noise from a measurement to isolate the contribution of the source of interest.

Which formulas does the tool use?

The sum is logarithmic and energetic: L_tot = 10·log₁₀(Σ 10^(Lᵢ/10)). The background-noise correction is L_corr = 10·log₁₀(10^(L_mis/10) − 10^(L_bg/10)), with the ISO 1996-2 thresholds. Reliability depends on ΔL = L_mis − L_bg: above 10 dB the correction is negligible, between 3 and 10 dB it is applicable, below 3 dB the result is only an upper bound (L_mis − 3 dB).

Logarithmic sum of N levels:

$$L_{\mathrm{tot}}=10{\log }_{10}\left(\sum _{i}10^{L_i/10}\right)$$

Background-noise subtraction:

$$L_{\mathrm{corr}}=10{\log }_{10}\left(10^{L_{\mathrm{mis}}/10}-10^{L_{\mathrm{bg}}/10}\right)$$

Reliability of the background correction, as a function of ΔL = L_mis − L_bg:

$$\{\begin{array}{ll}\Delta L>10\mathrm{dB}& \text{correction negligible,}{L}_{\mathrm{corr}}\approx L_{\mathrm{mis}}\\ 3\le \Delta L\le 10& \text{correction applicable}\\ \Delta L<3\mathrm{dB}& \text{unreliable: upper bound}{L}_{\mathrm{corr}}\le L_{\mathrm{mis}}-3\mathrm{dB}\end{array}$$

The three thresholds are those of ISO 1996-2 for environmental noise. The same subtraction appears in the sound power standards — ISO 3744 and ISO 3741 — with their own, stricter requirements on the background margin: the formula is the same, the scope is not, and a report should cite the standard of the field being measured.

The upper bound below 3 dB is not a convention: at ΔL = 3 dB the energetic subtraction is exactly −3.02 dB, and for smaller gaps the true value falls further. So «L_corr ≤ L_mis − 3 dB» is the strongest statement the data supports.

Terms

L_p — sound pressure level [dB], referenced to 20 µPa.

Spectral weightings (IEC 61672-1):

• A — approximates the ear’s response at moderate levels; it is the standard weighting for disturbance assessment and for most Italian and European regulations.
• C — flatter response; used for the peak level (L_Cpeak) and for low-frequency phenomena.
• Z — no weighting (“zero”), linear response 10 Hz – 20 kHz.

Levels with different weightings are not directly addable: summing an L_A with an L_Z yields a mathematically correct but physically meaningless number. The tool performs the sum anyway, raising the warning.

What are the tool’s limitations?

The logarithmic sum assumes incoherent sources; coherent sources (two loudspeakers in phase) can produce constructive or destructive interference and add differently. The background subtraction assumes L_bg is stationary and representative of the L_mis interval. For ΔL < 3 dB the source estimate is dominated by background uncertainty: the returned value is a bound, not a measurement.

• The logarithmic sum assumes incoherent sources. Coherent sources (e.g. two loudspeakers reproducing the same signal in phase) can produce constructive/destructive interference and add differently.
• The background subtraction assumes L_bg is stationary and representative of the L_mis interval.
• For ΔL < 3 dB the source estimate is dominated by background uncertainty: the returned value is a bound, not a measurement.

Standards & references

• ISO 1996-2:2017 — Description, measurement and assessment of environmental noise: determination of levels. The thresholds used here come from it — correction applicable between 3 and 10 dB of gap, negligible above, result unreliable below.
• ISO 3744:2025 — Determination of sound power levels of noise sources, engineering methods. It uses the same energetic subtraction with its own, stricter requirements on the background margin: it is the reference when measuring the sound power of a machine, not environmental noise.
• UNI 9884:1997 — Italian standard: acoustic characterisation of an area. Withdrawn without replacement: a historical reference, not current.
• IEC 61672-1:2013 — Sound level meters: A, C, Z weightings.

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