Source: https://guthlabs.ai/docs/instruments/beat-frequency-calculator/mechanism/

instrument mechanism / verified-clean

# Beat Frequency Calculator mechanism

The inspectable method record for Beat Frequency Calculator, kept separate from implementation and qualification.

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

## Model scope

The beat-frequency formula is correct, but the instrument claims a period output without specifying its formula or equal-frequency behavior, so the specification fails verification. The honest_label value "n/a" should be replaced with a disclosure of the required same-unit input convention and the undefined period when the input frequencies are equal.

- f_beat=|f1−f2| is the standard beat-frequency formula for two sinusoidal waves, assuming f1 and f2 are expressed in the same frequency units.

- The claimed period output has no formula. It should be T_beat=1/f_beat=1/|f1−f2| when f1≠f2.

- At f1=f2, f_beat=0 and the beat period is undefined rather than a finite value.

## Units and conventions

- f1 and f2 must use the same units, preferably Hz.

- If frequencies are in Hz, beat frequency is in Hz and beat period is in seconds.

- If frequencies are supplied in kHz, they must be converted consistently before computing, or the resulting period must be reported in milliseconds.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "f1": 440,
    "f2": 442,
    "unit": "Hz"
  },
  "expected_outputs": {
    "beat_frequency": 2,
    "beat_frequency_unit": "Hz",
    "period": 0.5,
    "period_unit": "s"
  },
  "working": "f_beat=|440−442|=|−2|=2 Hz. T_beat=1/f_beat=1/2=0.5 s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

Equal input frequencies produce a zero beat frequency, causing the period calculation 1/f_beat to divide by zero. Negative-frequency handling is also convention-dependent and can produce a materially different result if signed and unsigned interpretations are not distinguished.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/beat-frequency-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/beat-frequency-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/beat-frequency-calculator/qualification/>)

## 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`