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

instrument implementation / implementation-contract

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

A source-bound implementation contract for String/Wind Instrument Fundamental Frequency (String Length); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-133

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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"
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/string-wind-instrument-fundamental-frequency-string-length/mechanism/>)[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`