  We investigate the spectrum of photohadronically produced neutrinos at very
high energies (VHE, >10^14 eV) in astrophysical sources whose physical
properties are constrained by their variability, in particular jets in Active
Galactic Nuclei (blazars) and Gamma-Ray Bursts (GRBs). We discuss in detail the
various competing cooling processes for energetic protons, as well as the
cooling of pions and muons in the hadronic cascade, which impose limits on both
the efficiency of neutrino production and the maximum neutrino energy. If the
proton acceleration process is of the Fermi type, we can derive a model
independent upper limit on the neutrino energy from the observed properties of
any cosmic transient, which depends only on the assumed total energy of the
transient. For standard energetic constraints, we can rule out major
contributions above 10^19 eV from current models of both blazars and GRBs; and
in most models much stronger limits apply in order to produce measurable
neutrino fluxes. For GRBs, we show that the cooling of pions and muons in the
hadronic cascade imposes the strongest limit on the neutrino energy, leading to
cutoff energies of the electron and muon neutrino spectrum at the source
differing by about one order of magnitude. We also discuss the relation of
maximum cosmic ray energies to maximum neutrino energies and fluxes in GRBs,
and find that the production of both the highest energy cosmic rays and
observable neutrino fluxes at the same site can only be realized under extreme
conditions; a test implication of this joint scenario would be the existence of
strong fluxes of GRB correlated muon neutrinos up to ultra high energies,
>10^17 eV. Secondary particle cooling also leads to slightly revised estimates
for the neutrino fluxes from (non-transient) AGN cores.
