  Perturbation of a propagating crack with a straight edge is solved using the
method of matched asymptotic expansions (MAE). This provides a simplified
analysis in which the inner and outer solutions are governed by distinct
mechanics. The inner solution contains the explicit perturbation and is
governed by a quasi-static equation. The outer solution determines the
radiation of energy away from the tip, and requires solving dynamic equations
in the unperturbed configuration. The outer and inner expansions are matched
via the small parameter L/l defined by the disparate length scales: the crack
perturbation length L and the outer length scale l associated with the loading.
The method is first illustrated for a scalar crack model and then applied to
the elastodynamic mode I problem.
  The dispersion relation for crack front waves is found by requiring that the
energy release rate is unaltered under perturbation. The wave speed is
calculated as a function of the nondimensional parameter kl where k is the
crack front wavenumber, and dispersive properties of the crack front wave speed
are described for the first time. The example problems considered here
demonstrate that the potential of using MAE for moving boundary value problems
with multiple scales.
