When is the 20 log10 distance relation valid?

It is an ideal geometrical-spreading transfer for the same stable point-like source, the same sound-pressure-level descriptor and operating state, the same directivity sector, and two far-field receiver positions in a free field. It excludes reflections, barriers, ground effects, atmospheric absorption and meteorological effects.

Is this an ISO 9613-2 calculation?

No. ISO 9613-2:2024 is an outdoor engineering prediction method with octave-band source data and terms for geometrical divergence, atmospheric absorption, ground effect, reflections, screening and meteorology. This worksheet evaluates geometrical spreading only.

Can dB and dBA be used interchangeably?

No. The same fully identified acoustic descriptor, frequency weighting, time weighting or averaging interval, and source operating state must apply at both positions.

Does a road or any line source always lose 3 dB per distance doubling?

No. A fixed 3 dB rule is not a general model for roads or arbitrary extended sources. Source geometry, finite length, spectrum, ground, barriers and meteorology must be represented by a suitable validated method.

Can this result establish a safe distance or regulatory compliance?

No. It is not an exposure, dose, environmental-noise or compliance calculation. Those decisions require the applicable acoustic descriptor, measurement or a complete validated prediction, uncertainty and the governing requirements.

Reference worksheet · geometric spreading only

Ideal Free-Field Point-Source SPL Transfer

Transfer one explicitly identified sound-pressure-level descriptor between two distances using ideal spherical spreading. The result is conditional—not a complete outdoor-noise, indoor-noise, exposure, or compliance prediction.

same source statesame level descriptorfar fieldสนามเสียงอิสระ

Scope gate: use this worksheet only when both receiver positions meet every stated assumption. If ground, reflections, barriers, air absorption, weather, source directivity changes, near-field behaviour, or extended-source geometry matters, this single-term model is incomplete.

Recorded inputs

No example values are preloaded. Enter the measurement or documented source basis you actually have.

Acoustic level descriptor used at both positions Record the physical quantity plus frequency weighting/band, time weighting or averaging interval, as applicable. “dB” alone is not a descriptor.

Reference measurement/source record Identify the evidence behind L₁ so that unchanged operation, position and directivity can be checked.

Reference level L₁ (dB) A finite signed decimal is accepted. Use either decimal point or decimal comma.

Common distance unit Both distances must use this same unit; it cancels in the ratio.

Reference distance r₁ Positive source-to-receiver distance in the selected unit.

Target distance r₂ Positive source-to-receiver distance in the selected unit.

I have checked the model basis: one stable point-like source; unchanged operation and emission; the same level descriptor; both positions in the source’s far field and the same directivity sector; unobstructed free-field propagation; geometrical spreading is the only change being calculated.

Model and dimensional check

For spherical waves from an ideal point source in a lossless free field, far-field sound-pressure amplitude is proportional to 1/r. Therefore the pressure-level difference is:

G = 20 log₁₀(r₂/r₁)
L₂ = L₁ − G
ΔL = L₂ − L₁ = −20 log₁₀(r₂/r₁)

Here L₁ and L₂ are the same specified sound-pressure-level descriptor, in decibels; r₁ and r₂ are positive distances in the same unit. The ratio r₂/r₁ is dimensionless, so taking its logarithm is dimensionally valid. The associated ideal pressure-amplitude ratio is p₂/p₁ = r₁/r₂.

A doubling gives G = 20 log₁₀(2) = 6.0206 dB—not exactly 6 dB. If r₂ < r₁, G is negative and the model predicts an increase; the worksheet reports the sign rather than disguising it as “attenuation.”

Applicability checklist

เงื่อนไข	Required for this worksheet	If not satisfied
Source and operation	Same stable source power, spectrum and operating state	Do not attribute the observed difference solely to distance
Acoustic quantity	Same named level descriptor, weighting/band and time basis	Levels are not directly transferable
เรขาคณิต	Point-like at both distances; both points in the validated far field	Use a source/geometry-specific method
ทิศทาง	Same source directivity sector	Include documented directivity
Propagation	Free field; no relevant reflecting or screening objects	Model reflections, ground and barriers
Medium and weather	Their change is negligible over the path for the stated purpose	Use frequency-dependent atmospheric and meteorological modelling

“Far field” is not established here by a universal distance preset. It depends on source dimensions, wavelength, radiation behaviour and measurement purpose.

What this worksheet deliberately does not calculate

It does not calculate sound power level from sound pressure level.
It does not model a road, railway, pipe, façade or arbitrary “line source.” A universal 3 dB-per-doubling rule is not assigned to those cases.
It does not combine octave bands, A-weight a spectrum, or convert among instantaneous, maximum, peak, time-weighted, equivalent-continuous or exposure levels.
It does not include atmospheric absorption, ground effect, reflections, screens, foliage, buildings, terrain, wind or temperature gradients.
It does not establish a safe distance, worker dose, community-noise rating, legal limit or regulatory compliance.

Standards boundary and sources

Classification of the equation: general acoustical/physical relation for ideal spherical geometrical spreading. It is not presented as a formula prescribed by ISO 9613-2.

OSHA Technical Manual, Section III, Chapter 5 — official explanation of the point-source free-field distance relation and limits of real sound fields.
ISO 9613-2:2024, Edition 2 — current outdoor engineering method; its public scope lists geometrical divergence, atmospheric absorption, ground effect, reflections, screening and meteorology. A draft Amendment 1 is under development and is not used here.
ISO 9613-1:1993, Edition 1 — published, currently under review; frequency- and weather-dependent atmospheric absorption. No coefficients from its licensed text are reproduced here.
ISO 1996-1:2016, Edition 3 — current basic environmental-noise quantities and assessment procedures; its public note warns that the underlying acoustic quantity must be identified.
ISO 80000-8:2020, Edition 2 + Amendment 1:2025 — current names, symbols, definitions and units for acoustical quantities.
IEC 61672-1:2013, Edition 2 — sound-level-meter specifications distinguish frequency-weighted, time-weighted, time-averaged and sound-exposure measurements.

Official public records checked 13 July 2026. Clause-level ISO propagation algorithms and coefficients require the controlled standard text and are outside this worksheet.

Questions that prevent common misuse

Is “90 dB” enough information?

No. Record what level it is—for example a Z-weighted band level, L_Aeq,T, or another defined quantity—plus the relevant time/frequency basis and operating state. ISO 1996-1 explicitly warns that different acoustic quantities can all be expressed in dB and normally differ.

Can I use an A-weighted level?

Only as the same fully specified A-weighted descriptor at both positions and only when every propagation assumption is met. This worksheet applies the same frequency-independent geometrical term to the unchanged source spectrum; it does not calculate frequency-dependent losses or A-weight a spectrum.

Does the equation work indoors?

Not as a prediction of the total room level. Reflected/reverberant sound generally prevents the total level from following ideal spherical spreading. A separately isolated direct-field component may be analysed only with a defensible measurement model.

Why is there no line-source switch?

Because selecting “line source” does not prove cylindrical spreading. Real extended sources can be finite, incoherent or directional and can transition with distance; roads additionally require traffic, spectrum, ground, screening and meteorology. A generic switch would produce unjustified precision.

Can this choose a hearing-safe distance?

No. Hearing risk depends on the applicable A-weighted or peak descriptor, duration, temporal pattern, multiple sources and governing requirements. Verify exposure using suitable measurements or a complete validated assessment.