Section 9.1 - Wave Equation * enough already with the string equation * 3-d waves - another application of stress and strain tensor ~ Strain tensor: formed from changes in the displacement field along different directions ~ Newton’s law: stress causes transfer of momentum or acceleration ~ Hooke’s law: relation between stress (force) and strain (stretch) ~ combine these to derive the wave equation for u(x,t) * P-wave: * S-wave: * mode-conversion: Zoeppritz eq’s (mech. equivalent of Frenel eq’s) NOTE: no relation whatsoever to H-atom S (l=0) and P (l=1) -waves Lamé’s 1st param (~pres.) Lamé’s 2nd param (sheer) Poisson’s ratio P-wave (longitudinal) modulus S-Wave (sheer,trans) modulus Young’s modulus Bulk Modulus Elastic moduli (homogeneous, isotropic): for fluids air: v=343 m/s @20degC water: v=1482 m/s steel: v=5960 m/s (Wikipedia)