Composite materials pose a complex problem for ultrasonic nondestructive evaluation due to their unique material properties, greater damping, and often complicated geometry. In this study, we explored acoustic wavenumber spectroscopy (AWS) as a means of rapid inspection of laminate and honeycomb composites. Each aerospace sample was tested at different ultrasonic frequencies using steady-state excitation via a piezo electric actuator. We measured the velocity response of the composite at each pixel via a raster scan using a laser Doppler vibrometer. We were able to detect radial inserts along corners, delamination, and facing-core separation by analyzing local amplitude and wavenumber responses. For each honeycomb composite, we excited the sample at the first resonant frequency of the individual cells. The local mode shape for each cell was extracted from the local amplitude response. Analyzing local amplitude and phase responses for each cell provided an accurate indication as to the presence, size, shape, and type of defect present in the composite. We detected both delamination and deformation of cells within a honeycomb composite. For the laminar composites, we analyzed the non-resonance steady-state response at several excitation frequencies.