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87 + 1 . 873 These ratios show that the longitudinal wave is usually the fastest, and that the shear wavespeed is about half that. The Rayleigh wavespeed is a little slower than the shear wavespeed. , waves propagating along an axis of symmetry) as described in Appendix 3. For arbitrary directions in an anisotropic material, a numerical method must be used to calculate the wavespeed, as described in Appendix 9. , viscoelastic or fluid media, or for high-amplitude stress waves or waves near a boundary, the wavespeed may depend on the frequency and other parameters such as dimensions.
At the peak stress, when there is no motion, the energy is entirely potential, and at the peak velocity when the stress is zero, the energy is entirely kinetic. The energy is supplied by the source of the wave and is carried with it. It is reduced by processes which dissipate it as heat, through compression, viscosity, plasticity, etc. W h e n these processes are small, the wave propagates a long way, but generally the wave decays in a moderate distance. W H A T ARE T H E U N I T S OF E L A S T I C I T Y , D E N S I T Y , A N D WAVESPEED?
There are two types of such waves, the longitudinal and the transverse. There are also two boundary configurations which produce unique easily measured wavespeeds with simple formulas. These are the axial wave in a slender rod and the Rayleigh wave on a free surface. The simplest wavespeeds to measure, and those having the simplest formulas, are for axial and torsional (shear) propagation along a bar: r -- ( E / p ) l/2 Cs = ( G / p ) 1 / 2 where Cb is the bar wavespeed, Cs is the shear wavespeed, E -- p c 2 is the Young's modulus of elasticity, G = p c 2 is the shear modulus, and p is the density.