Source: https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/mechanism/

instrument mechanism / verified-clean

# String/Wind Instrument Fundamental Frequency (String Length) mechanism

The inspectable method record for String/Wind Instrument Fundamental Frequency (String Length), kept separate from implementation and qualification.

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

## Model scope

The mathematical formula is correct for an ideal flexible string under uniform tension with fixed endpoints. The honest-label statement appropriately identifies the main physical limitation, but the catalog specification must explicitly define the units for length, tension, and linear mass density before release.

- The formula f=(1/(2L))*sqrt(T/µ) is the standard ideal flexible-string fundamental-frequency formula, but the specification does not define input units, making application ambiguous.

## Units and conventions

- Length L must be in metres.

- Tension T must be in newtons.

- Linear mass density µ must be in kilograms per metre.

- With these SI units, sqrt(T/µ) has units of metres per second, and division by 2L produces hertz.

- All test-vector values are interpreted using the units explicitly supplied in each input object.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "length": 0.5,
    "length_unit": "m",
    "tension": 100,
    "tension_unit": "N",
    "linear_mass_density": 0.01,
    "linear_mass_density_unit": "kg/m"
  },
  "expected_outputs": {
    "fundamental_frequency_Hz": 100
  },
  "working": "f=(1/(2L))*sqrt(T/µ)\nf=(1/(2*0.5))*sqrt(100/0.01)\nf=(1/1)*sqrt(10000)\nf=1*100\nf=100 Hz"
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

Zero length and zero linear mass density produce division-by-zero, while negative tension produces a non-real square-root argument. The specification also lacks an explicit unit convention, allowing a 100-fold frequency discrepancy for the same numeric length.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`