  A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D
periodic materials is reported. The approach uses a monodromy-matrix operator
to enable direct integration in one of the coordinates and exponentially fast
convergence in others. As a result, the solution for $c$ has a more closed form
than previous formulas. It significantly improves the efficiency and accuracy
of evaluating $c$ for high-contrast composites as demonstrated by a 2D example
with extreme behavior.
