AbstractWe consider the Dirichlet problem for the reduced wave equation ΔUx+x2Ux= 0 in a two‐dimensional exterior domain with boundaryC, whereCconsists of a finite number of smooth closed curvesC1,…,Cm. The question of interest is the behavior ofUxas ϰ → 0. We show thatUconverges to the solution of the corresponding exterior Dirichlet problem of potential theory if the boundary data converge to a limit uniformly onC.This generalizes a well‐known result of R. C. MacCamy for the