Source: https://guthlabs.ai/docs/instruments/sound-intensity-decibel-level-calculator/

instrument / verified-clean

# Sound Intensity & Decibel Level Calculator

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-intensity-decibel-level-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/sound-intensity-decibel-level-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/sound-intensity-decibel-level-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/sound-intensity-decibel-level-calculator/qualification/>)

## Ledger state

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

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-5

**Evidence ID**: t5-105

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formulas themselves are correct under the stated free-field point-source assumptions. The product should be labeled as a sound intensity level calculator, distinct from SPL/microphone dB, electronic voltage-ratio dB, and power-ratio dB. Clarify the mutually exclusive input modes and enforce SI-unit conversion before calculation.

### Formula and scope findings

- The formulas are mathematically standard for sound intensity level and an isotropic free-field point source, but distance alone is insufficient: distance-based calculation requires acoustic power P and a specified source model.

- The input contract is ambiguous about whether the user supplies intensity, power plus distance, or both, and which value takes precedence if both are supplied.

- β=10log10(I/I0) computes sound intensity level, not sound pressure level (SPL); the product label must not imply microphone/SPL dB without additional pressure-based inputs and calibration.

### Unit assumptions

- P must be total acoustic power in watts (W).

- r must be source distance in meters (m), and must satisfy r>0.

- I must be in watts per square meter (W/m²).

- I0=1e-12 W/m² is the standard reference intensity for sound intensity level.

- The inverse-square relation assumes an omnidirectional point source radiating uniformly into a free field.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The exact zero-distance input produces division by zero and must be rejected; additionally, an unspecified distance unit can shift the reported level by 40 dB for the same numeric input.

## 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": {
    "mode": "power_and_distance",
    "power_W": 1,
    "distance_m": 1
  },
  "expected_outputs": {
    "intensity_W_per_m2": 0.0795774715,
    "level_dB": 109.0079
  },
  "working": "4πr² = 4×3.14159265×1² = 12.5663706. I = P/(4πr²) = 1/12.5663706 = 0.0795774715 W/m². I/I0 = 0.0795774715/(1e-12) = 7.95774715e10. β = 10log10(7.95774715e10) = 10×10.900790 = 109.0079 dB."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## 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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`