  We study the vibrational spectra of one-dimensional statically compressed
granular crystals (arrays of elastic particles in contact) containing defects.
We focus on the prototypical settings of one or two spherical defects
(particles of smaller radii) interspersed in a chain of larger uniform
spherical particles. We measure the near-linear frequency spectrum within the
spatial vicinity of the defects, and identify the frequencies of the localized
defect modes. We compare the experimentally determined frequencies with those
obtained by numerical eigen-analysis and by analytical expressions based on
few-site considerations. We also present a brief numerical and experimental
example of the nonlinear generalization of a single-defect localized mode.
