  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.
