Source: https://guthlabs.ai/docs/instruments/sound-level-distance-attenuation-inverse-square-law/

instrument / verified-clean

# Sound Level Distance Attenuation (Inverse Square Law)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/sound-level-distance-attenuation-inverse-square-law/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/sound-level-distance-attenuation-inverse-square-law/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/sound-level-distance-attenuation-inverse-square-law/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/sound-level-distance-attenuation-inverse-square-law/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Audio, Music, Photography & Color

**Tranche**: tranche-2

**Evidence ID**: t2-013

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formula is correct for an ideal omnidirectional point source in a free field. Exact ambiguity requiring review: the spec does not explicitly define the SPL reference/weighting and does not specify required distance units or the positive-distance constraint. The honest label should also mention that source directivity, near-field effects, and atmospheric absorption are excluded if those conditions matter.

### Formula and scope findings

- SPL2=SPL1-20log10(d2/d1) is the standard free-field point-source relationship when both distances are positive and expressed in the same units.

- +6 dB per halving is a rounded approximation; the exact change is +6.0206 dB per halving distance.

- The specification does not explicitly state that the reference level is dB SPL measured with the same frequency weighting and bandwidth as the target level.

### Unit assumptions

- Reference SPL and output are dB SPL referenced to 20 micropascals.

- Reference distance and target distance must use the same length units; only their ratio is used.

- Distances must be strictly greater than zero.

- The source is treated as an ideal point source in a free field, with unchanged source output, frequency content, and measurement conditions.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not explicitly state that both reference and target distances must be strictly positive. A zero reference distance produces division by zero and an undefined logarithm, so an implementation without domain validation can fail or emit a non-finite result.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "reference_spl_db_spl": 74,
    "reference_distance_m": 2,
    "target_distance_m": 8
  },
  "expected_outputs": {
    "target_spl_db_spl": 61.96
  },
  "working": "d2/d1 = 8/2 = 4. log10(4) = 0.60206. Distance loss = 20 x 0.60206 = 12.0412 dB. SPL2 = 74 - 12.0412 = 61.9588 dB SPL, approximately 61.96 dB SPL."
}
````

## Related workflows

[Audio Engineer's Rackplacement levels](<https://guthlabs.ai/docs/instrument-workflows/audio-rack/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`