Past exam of the mathematics course of the University of Cambridge 2023 ii Paper 2 40C b ii Solution Created 2026-09-24 Updated 2026-09-25
Average the instantaneous elastic-wave energy flux over one temporal period at fixed position. For complex amplitudes,Write the evanescent P displacement amplitude asFor an isotropic linear elastic material with Lamé parameters , its stress and velocity amplitudes areApart from a real common factor,which is purely imaginary. Its real part vanishes, and henceThe converted P-wave is a reactive near-boundary field and transports no time-averaged acoustic energy in the normal direction.