  We present a derivation of the transverse force acting on a hydrodynamic
vortex in the presence of an incoming sound wave from a global solution of the
scattering problem, using the method of matched asymptotic expansions. The
solution presented includes a detailed treatment of the interaction of the
incident wave with the vortex core, and is free from the singularities in the
momentum exchange between vortex and sound wave which have led to contradictory
results for the value of the transverse force in the literature.
