Pulse-echo measurements on a block of an unidentified metal

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

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

Problem

Pulse-echo measurements on a block of an unidentified metal, density ρ=8900 kg m−3\rho = 8900\,\mathrm{kg\,m^{-3}}, give bulk wave speeds cL=5.30 km s−1c_L = 5.30\,\mathrm{km\,s^{-1}} and cT=2.70 km s−1c_T = 2.70\,\mathrm{km\,s^{-1}}. ((a)) Find the shear modulus GG and the first Lamé constant λ\lambda from the two speeds. ((b)) Using the isotropic relation between the bulk modulus and the Lamé constants, K=λ+23GK = \lambda + \tfrac23G, find KK.

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