A plane P wave in a Poisson solid (

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Superposition, boundaries and interference

Bending, Ringing, Breaking and Flowing, Ch Elastic waves in a solid and at its surface

Problem

A plane P wave in a Poisson solid (ν=0.25\nu = 0.25, so cL/cT=3c_L/c_T = \sqrt3) strikes a stress-free plane surface at an angle of incidence θP=70∘\theta_P = 70^\circ from the normal. ((a)) Find the angle θS\theta_S of the reflected SV wave. ((b)) Using the free-surface reflection coefficient RPP=sin⁡2θPsin⁡2θS−(cL/cT)2cos⁡22θSsin⁡2θPsin⁡2θS+(cL/cT)2cos⁡22θS,R_{PP} = \frac{\sin2\theta_P\sin2\theta_S - (c_L/c_T)^2\cos^22\theta_S}{\sin2\theta_P\sin2\theta_S + (c_L/c_T)^2\cos^22\theta_S}, obtained from the two traction-free boundary conditions, decide whether any energy returns as P, and state what fraction of the incident energy leaves as SV.

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