We observe and characterize the scattering of acoustic wave packets by a sunspot, in a regime where the wavelength is comparable to the size of the sunspot. Spatial maps of wave traveltimes and amplitudes are measured from the cross-covariance function of the random wave field. The averaging procedure is such that incoming wave packets are plane wave packets. Observations show that the magnitude of the traveltime perturbation caused by the sunspot diminishes as waves propagate away from the sunspot -- a finite-wavelength phenomenon known as wavefront healing. Observations also show a reduction of the amplitude of the waves after their passage through the sunspot. A significant fraction of this amplitude reduction is due to the defocusing of wave energy by the fast wave-speed perturbation introduced by the sunspot. This ``geometrical attenuation'' will contribute to the wave amplitude reduction in addition to the physical absorption of waves. In addition, we observe an enhancement of wave amplitude away from the central path: diffracted rays intersect with unperturbed rays (caustics) and wavefronts fold and triplicate. Thus we find that ray tracing is useful to interpret these phenomena, although it cannot explain wavefront healing.