Sound Intensity & Decibel Level Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

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

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json