Past exam of the mathematics course of the University of Cambridge 2023 ii Paper 2 40C b i Solution Created 2026-09-24 Updated 2026-10-03
The reflected P-wave is propagating only while its normal wavenumber is real, equivalently while . Sinceit is evanescent whenPutThen its spatial factor iswhich decays as . The reflected SV amplitude becomesThe numerator and denominator have equal complex modulus, soThus evanescent mode conversion changes the reflected SV phase but not its amplitude, as described by Unit-modulus SV reflection with evanescent P conversion.