  For the inverse source problem with the two-dimensional Helmholtz equation,
the singular values of the 'source-to-near field' forward operator reveal a
sharp frequency cut-off in the stably recoverable information on the source. We
prove and numerically validate an explicit, tight lower bound for the spectral
location of this cut-off. We also conjecture and support numerically a tight
upper bound for the cut-off. The bounds are expressed in terms of zeros of
Bessel functions of the first and second kind.
