= Solid-fluid P-wave transmission coefficient
{title2=$T_P=\frac{2\rho\alpha_f\cos2\theta_S\cos\theta_P}{\rho_f\alpha_f\cos\theta_P+\rho\alpha E\cos\theta_f}$}
For incidence from a solid with compressional/shear speeds $\alpha,\beta$ into a fluid of sound speed $\alpha_f$, let $E=\cos^22\theta_S+(\beta^2/\alpha^2)\sin2\theta_P\sin2\theta_S$. The displayed coefficient multiplies the transmitted <displacement field> potential relative to the incident <P wave> potential, using the same retarded-time waveform. <Snell law for elastic and acoustic waves> matches the tangential slowness. Continuity of normal <displacement field>, zero tangential <traction>, and continuity of normal <traction> give the coefficient. It is not a displacement-amplitude coefficient: longitudinal <displacement field> acquires an additional ratio $\alpha/\alpha_f$.
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