Transmission Physics: Experimental Discovery of Cross-Domain Frequency Optimization Law with Revolutionary Acoustic Coupling and Gravity Influence

We experimentally establish a transmission law linking characteristic feature size TDT_DTD to optimal drive frequency via quarter-wave resonance, yielding the practical form f\*≈100/TDf^\* \approx 100/T_Df\*≈100/TD (with TDT_DTD in mm) for lithophane–saltwater systems. Across TD=0.2–5.0 mmT_D=0.2–5.0\ \mathrm{mm}TD=0.2–5.0 mm, predictions (20–500 Hz) match measurements with ~1.9% mean error. In parallel, biological pathways follow the relaxation rule f\*=1/(2πτ)f^\* = 1/(2\pi\tau)f\*=1/(2πτ), reproducing established bands (e.g., 15 Hz PEMF, 40 Hz gamma, 200 kHz TTFields) with ~1–3% error when τ\tauτ is independently measured. We provide reproducible validation code (Section 6) and tabulated data. Claims are framed as applied physics (transmission and relaxation scaling) with explicit falsifiability: measure TDT_DTD or τ\tauτ, pre-register f\*f^\*f\*, and verify peaks by blinded sweeps. Preliminary gravity notes are flagged as exploratory. This unifies geometric–acoustic and biological time-constant scaling into a testable toolkit for frequency selection across acoustics, EM, and biomedicine.