  The problem of the fictitious frequency spectrum resulting from numerical
implementations of the boundary element method for the exterior Helmholtz
problem is revisited. When the ordinary 3D free space Green's function is
replaced by a modified Green's function, it is shown that these fictitious
frequencies do not necessarily have to correspond to the internal resonance
frequency of the object. Together with a recently developed fully
desingularized boundary element method that confers superior numerical
accuracy, a simple and practical way is proposed for detecting and avoiding
these fictitious solutions. The concepts are illustrated with examples of a
scattering wave on a rigid sphere.
