Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for $rho v^2$, where $rho$ is the mass density and v the wave speed, in terms of the elongation $e$ of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: $rho v^2 = a + be + ce^2$, say, $a$ depends linearly on $mu$; $b$ on $mu$ and $A$; and $c$ on $mu$, $A$, and $D$, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.
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