{"query": "The wave equation for sound", "count": 20, "results": [{"id": "card_works_acoustics", "title": "The wave equation for sound", "shelf": "the-works", "surface": "secular", "snippet": "For any wave, speed = frequency × wavelength. A 343 Hz tone with a one-metre wavelength travels at 343 m/s — the speed of sound in air.  Worked & sealed by the engine — c = f·λ = 343·1 = 343 m/s.  [HO", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_differential_equations", "title": "Differential equations (the language every physical law is written in)", "shelf": "theories", "surface": "secular", "snippet": "Differential equations (the language every physical law is written in) — an engine domain that can touch it: mathematics. Calibration: seals — solutions verify by substitution; specific integrations c", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_acoustic_wave_theory", "title": "Acoustic wave theory (harmonics, Doppler)", "shelf": "theories", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) — an engine domain that can touch it: acoustics. Calibration: seals — frequencies, harmonics and Doppler shifts compute. Sound is a PRESSURE wave in a medium,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_wave_optics", "title": "Wave optics (Huygens, Snell's law, diffraction)", "shelf": "theories", "surface": "secular", "snippet": "Wave optics (Huygens, Snell's law, diffraction) — an engine domain that can touch it: optics. Calibration: seals — refraction, lens and diffraction relations compute. Light behaves as a wave: it refra", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_maxwell_s_equations_classical_electromagnetism", "title": "Maxwell's equations / classical electromagnetism", "shelf": "theories", "surface": "secular", "snippet": "Maxwell's equations / classical electromagnetism — an engine domain that can touch it: electrical. Calibration: partial — circuit and field relations verify; the full field theory is map-only. Four eq", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_seismology_earthquake_magnitude", "title": "Seismology & earthquake magnitude (Richter / moment)", "shelf": "theories", "surface": "secular", "snippet": "Seismology & earthquake magnitude (Richter / moment) — an engine domain that can touch it: geology. Calibration: seals — magnitude and energy relations compute. Earthquakes radiate P waves (fast, comp", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_general_relativity", "title": "General relativity", "shelf": "theories", "surface": "secular", "snippet": "General relativity — an engine domain that can touch it: physics. Calibration: partial — specific relations verify; the field equations as a whole are map-only. Gravity is not a force but the CURVATUR", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_dimensional_analysis", "title": "Dimensional analysis & similarity (Buckingham Π)", "shelf": "theories", "surface": "secular", "snippet": "Dimensional analysis & similarity (Buckingham Π) — an engine domain that can touch it: physics. Calibration: seals — dimensional consistency and Π-group counts check exactly. Any true physical equatio", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_heat_transfer", "title": "Heat transfer (conduction, convection, radiation)", "shelf": "theories", "surface": "secular", "snippet": "Heat transfer (conduction, convection, radiation) — an engine domain that can touch it: thermodynamics. Calibration: seals — Fourier's law, R-values and Stefan–Boltzmann all compute. Heat moves three ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_heisenberg_uncertainty_principle", "title": "Heisenberg uncertainty principle", "shelf": "theories", "surface": "secular", "snippet": "Heisenberg uncertainty principle — an engine domain that can touch it: physics. Calibration: partial — the bound computes; the ontology is map-only. Δx·Δp ≥ ħ/2. Position and momentum cannot both be s", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__wave_optics", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  Wave optics (Huygens, Snell's law, diffraction)", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and Wave optics (Huygens, Snell's law, diffraction) are the same form in different domains. both are the wave equation in different media: Huygens' constructi", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_maxwells_equations", "title": "Maxwell's equations — the first unification", "shelf": "codex", "surface": "secular", "snippet": "Electricity, magnetism and light are one electromagnetic field, and its waves travel at the speed of light (c = 1/sqrt(mu0 eps0), sealed on stick_maxwell_s_equations_and_superconductivity). The archet", "authority_tier": "engine_derived", "source": "Narrow Highway — Maxwell's equations", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__electromagnetic_spectrum", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  The electromagnetic spectrum & modulation (radio to gamma, one axis)", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and The electromagnetic spectrum & modulation (radio to gamma, one axis) are the same form in different domains. identical wave mathematics on a different car", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_elasticity__acoustic_wave_theory", "title": "Bridge: Elasticity (Hooke's law, stress–strain)  ↔  Acoustic wave theory (harmonics, Doppler)", "shelf": "bridges", "surface": "secular", "snippet": "Elasticity (Hooke's law, stress–strain) and Acoustic wave theory (harmonics, Doppler) are the same form in different domains. Hooke's linear restoring force gives the harmonic oscillator, and a contin", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_em_wave", "title": "Electromagnetic waves", "shelf": "calculations", "surface": "secular", "snippet": "Electromagnetic waves — electrical. Formula: d2E/dt2 = c^2 laplacian(E). Canonical FORM: wave (d2u/dt2 = c^2 * laplacian(u)) — light is Maxwell's equations in wave form. Same form, different domain: t", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_dual_wave__fourier_spectral", "title": "Duality: wave  ↔  fourier_spectral  (superposition of frequencies)", "shelf": "bridges", "surface": "secular", "snippet": "A deep bridge between two forms — superposition of frequencies. every wave is a superposition of pure frequencies; the wave equation is solved in the spectral domain", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_master_modular_exponentiation", "title": "Master equation: c = a^k mod n", "shelf": "bridges", "surface": "secular", "snippet": "the one-way power at the root of the discrete world: raising to a power modulo n is cheap, but inverting it — recovering the exponent, or factoring n — is hard on a classical machine and easy on a qua", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_a7ae37960cae", "title": "FM broadcast (VHF) — three-meter waves, line of sight", "shelf": "science", "surface": "secular", "snippet": "88–108 MHz; sealed: the 100 MHz wave is 2.99 m, and its quarter-wave whip is 74 cm —\nthe length of a car antenna, derived: https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_comms_antenna_basics", "title": "Antennas — the cheapest way to double your range", "shelf": "communications", "surface": "secular", "snippet": "A better antenna beats more power almost every time. Key ideas: HEIGHT wins for VHF/UHF — they go line-of-sight, so raising the antenna a few metres can double reach. Length matters: a common field an", "authority_tier": "reference", "source": "U.S. Army field antenna & signaling references (public domain)", "readable": false, "generated": false}, {"id": "card_sys_wave", "title": "Waves & oscillation", "shelf": "systems", "surface": "secular", "snippet": "The same wave equation governs sound in air, light in the field, ripples on water, and a plucked string. The same harmonic oscillator is an LC circuit, a mass on a spring, and a pendulum — resonance a", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_works_acoustics"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}