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Comparison of longitudinal, Rayleigh, and shear wave speeds for an isotropic linear elastic medium, plotted as a function of
Poisson ratio. The medium is assumed to have only two independent elastic constants, which can be cast as the Young's modulus E and the Poisson ratio {\displaystyle \nu }. The
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Rayleigh speed curve shown is an approximation to the analytic solution, with the error growing as the
Poisson ratio is lowered. The small discrepancy from the analytic solution is about 0.01 {\sqrt(E/\rho)} at {\nu=0}, where the error is maximal.
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