  We consider the inverse source problem of a fixed wavenumber: study
properties of an acoustic source based on a single far- or near-field
measurement. We show that nonradiating sources having a convex or non-convex
corner or edge on their boundary must vanish there. The same holds true for
smooth enough transmission eigenfunctions. The proof is based on an energy
identity from the enclosure method and the construction of a new type of planar
complex geometrical optics solution whose logarithm is a branch of the square
root. The latter allows us to deal with non-convex corners and edges.
