  In glasses and other disordered materials, measurements of the vibrational
density of states reveal that an excess number of long-wavelength
(low-frequency) modes, as compared to the Debye scaling seen in crystalline
materials, is associated with a loss of mechanical rigidity. In this paper, we
present a novel technique for measuring the density of modes (DOM) in a real
granular material, in which we mimic thermal excitations using white noise
acoustic waves. The resulting vibrations are detected with piezoelectric
sensors embedded inside a subset of the particles, from which we are able to
compute the DOM via the spectrum of the velocity autocorrelation function, a
technique previously applied in thermal systems. The velocity distribution for
individual particles is observed to be Gaussian, but the ensemble distribution
is non-Gaussian due to varying widths of the individual distributions. In spite
of this deviation from a true thermal system, we find that the DOM exhibits
several thermal-like features, including Debye scaling in a compressed
hexagonally ordered packing, and an increase in low-frequency modes as the
confining pressure is decreased. In disordered packings, we find that a
characteristic frequency $f_c$ increases with pressure, but more weakly than
has been observed in simulations of frictionless packings.
