Source: https://guthlabs.ai/docs/instruments/standing-wave-harmonics-calculator-strings-pipes/
instrument / verified-clean
# Standing Wave Harmonics Calculator (strings & pipes)
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-6
**Evidence ID**: t6-087
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The core frequency formulas are correct for the stated ideal boundary conditions. The instrument needs an explicit wavelength formula, a defined harmonic-table range, validation rules for L, v, and n, and documented speed-of-sound table conditions before release.
### Formula and scope findings
- The stated frequency formulas are standard: f_n = nv/(2L) for a string with both ends fixed and an open pipe, and f_n = (2n−1)v/(4L) for a pipe closed at one end.
- The claimed wavelength output has no specified formula; it should use λ = v/f_n, giving λ = 2L/n for strings/open pipes and λ = 4L/(2n−1) for closed pipes.
- The harmonic-series table has no specified range or maximum harmonic number, so its output is ambiguous.
- For a closed pipe, n must be the positive mode index n = 1,2,3,...; these correspond to the first, third, fifth, ... harmonics, not all integer harmonics.
- The speed-of-sound table is underspecified unless its medium, temperature, and environmental assumptions are defined. No frequency formula itself is incorrect.
### Unit assumptions
- L must be positive and expressed in a length unit compatible with v; v must be expressed in the corresponding length unit per second.
- n is dimensionless and must be a positive integer.
- For strings and open pipes, the stated formula assumes ideal 1D standing waves with nodes at both string ends or antinodes at both pipe ends.
- For closed pipes, the formula assumes one pressure node and one pressure antinode, with only odd modes present.
- Wavelength is in the same length unit as L because λ = v/f_n.
- The supplied speed-of-sound value must correspond to the selected medium and conditions; air speed varies with temperature and other environmental factors.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
A zero-length input produces division by zero and undefined frequency. The instrument must reject L=0; otherwise it can emit an invalid result or fail. Signed wave speed also exposes a convention hazard because literal substitution yields a negative frequency.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"boundary_type": "string_both_ends_fixed",
"L": 0.65,
"L_unit": "m",
"v": 130,
"v_unit": "m/s",
"n": 3,
"harmonic_table_through_n": 3
},
"expected_outputs": {
"f_n_Hz": 300,
"wavelength_m": 0.4333333333,
"harmonic_series": [
{
"n": 1,
"f_Hz": 100,
"wavelength_m": 1.3
},
{
"n": 2,
"f_Hz": 200,
"wavelength_m": 0.65
},
{
"n": 3,
"f_Hz": 300,
"wavelength_m": 0.4333333333
}
]
},
"working": "String formula: f_3 = (3×130)/(2×0.65) = 390/1.30 = 300 Hz. Wavelength: λ_3 = v/f_3 = 130/300 = 0.4333333333 m, equivalently 2L/n = (2×0.65)/3 = 1.30/3 = 0.4333333333 m. Table: n=1 gives 130/1.30 = 100 Hz; n=2 gives 260/1.30 = 200 Hz; n=3 gives 390/1.30 = 300 Hz."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`