String/Wind Instrument Fundamental Frequency (String Length) mechanism

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

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