Level-domain engineering worksheet
Acoustic Level Summation
Choose the physical model before adding decibels: incoherent pressure contributions, independent source sound powers, or coherent same-frequency pressure vectors.
Documented components
All fields start blank. Use each physical component once; do not count shared background repeatedly.
Conditional result
Model 1 — mutually incoherent pressure contributions
For compatible mean-square sound-pressure levels from mutually incoherent simultaneous components at one receiver, the cross terms average to zero:
Every Lᵢ must be the same descriptor: for example, all LAeq,15min at one receiver over the same interval, or all levels in the same one-third-octave band. Two equal incoherent components add exactly 10 log₁₀(2) = 3.0103 dB.
Model 2 — independent source sound powers
Independent acoustic powers add linearly, so compatible sound-power levels use the same 10 log₁₀ expression:
The output remains a sound-power level. It is not a receiver sound-pressure level and does not include directivity, distance, propagation, reflections or source interaction. If operating sources change one another’s emission, separately measured powers are not an independent-source model.
Model 3 — coherent same-frequency pressure components
For stable coherent tones at the same frequency and receiver, convert each pressure level to a relative amplitude and add complex pressure vectors:
Lp,Σ = 20 log₁₀|pΣ/p₀|
Two equal in-phase components add 6.0206 dB; equal quadrature components add 3.0103 dB; ideal equal components 180° apart cancel. Real acoustic phase varies with frequency and position, so this mode is not valid for broadband levels, unstable phase, partial coherence or spatial averaging.
Compatibility and exclusion table
| Question | Required answer | If not established |
|---|---|---|
| Same physical quantity and reference? | Yes: Lp with Lp, or Lw with Lw | Do not sum |
| Same weighting/band and time descriptor? | Yes | Reprocess the underlying data first |
| Same receiver and simultaneous pressure basis? | Yes for pressure modes | Do not present the result as a receiver total |
| Shared background counted once? | Removed, negligible, or explicitly isolated | Inputs can double-count energy |
| Correlation/coherence known? | Supported by the selected model | Cross-spectral information is required |
| Occupational exposure decision intended? | No—this is level summation only | Use a duration-based framework-specific exposure assessment |
Sources and standards boundary
Equation classification: general logarithmic level relations derived from linear energy/power addition or coherent pressure superposition. They are not labelled as an ISO compliance calculation.
- OSHA Technical Manual, Section III, Chapter 5, Appendix B.3 — official 10 log₁₀ summation of compatible pressure, intensity or power levels.
- NIOSH Industrial Noise Control Manual — random-noise assumption and simultaneous-source energy addition.
- NIST Special Publication 811 — 20 log₁₀ field-quantity and 10 log₁₀ power-quantity level definitions and the requirement to state the reference.
- Boston University, The Decibel Scale — public instructional derivation distinguishing coherent amplitude addition from incoherent intensity addition.
- ISO 80000-8:2020, Edition 2 + Amendment 1:2025 — current names, symbols, definitions and units for acoustical quantities.
- IEC 61672-1:2013, Edition 2 — distinguishes frequency-weighted, time-weighted, time-averaged and exposure sound-level measurements.
Official records checked 13 July 2026. Partial-coherence cross terms, background-correction procedures and closed standard clauses are not guessed here.
Questions that prevent common errors
Can I mix dB and dBA?
No. “dB” alone does not identify the measured quantity or weighting. All inputs must have the same explicitly recorded descriptor.
Can I add measurements made with each machine on while the same background remains?
Not directly. Each reading then contains the background, so adding them counts that energy repeatedly. Use source-only contributions obtained through a justified isolation/background method, or measure the simultaneous total.
Can I add sequential tasks to obtain daily exposure?
Not with this simultaneous-source worksheet. Sequential exposure periods require duration-weighted energy integration or the formula specified by the governing exposure framework.
Why can a coherent result be below every component?
Coherent pressures can interfere destructively. The result depends on relative phase at the specific receiver and frequency; it is not an energy sum.
Is there an 85 dBA hearing-protection line?
No. A source-level sum is not automatically an eight-hour occupational exposure. OSHA, NIOSH and EU action/limit quantities differ and require duration and framework-specific assessment.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
