  The origin of boson peak -- an excess of density of states over Debye's model
in glassy solids -- is still under intense debate, among which some theories
and experiments suggest that boson peak is related to van-Hove singularity.
Here we show that boson peak and van-Hove singularity are well separated
identities, by measuring the vibrational density of states of a two-dimensional
granular system, where packings are tuned gradually from a crystalline, to
polycrystals, and to an amorphous material. We observe a coexistence of well
separated boson peak and van-Hove singularities in polycrystals, in which the
van-Hove singularities gradually shift to higher frequency values while
broadening their shapes and eventually disappear completely when the structural
disorder $\eta$ becomes sufficiently high. By analyzing firstly the strongly
disordered system ($\eta=1$) and the disordered granular crystals ($\eta=0$),
and then systems of intermediate disorder with $\eta$ in between, we find that
boson peak is associated with spatially uncorrelated random flucutations of
shear modulus $\delta G/\langle G \rangle$ whereas the smearing of van-Hove
singularities is associated with spatially correlated fluctuations of shear
modulus $\delta G/\langle G \rangle$.
