A model of parametric transmitting antenna in granular media is developed, which takes into account velocity dispersion, frequency-dependent absorption, and frequency-dependent scattering of acoustic waves in granular media. The latter process may induce a transition from the ballistics to the diffusion regime of pump (primary) high-frequency wave propagation with increasing frequency. The conditions under which the transition from ballistics to diffusion manifests itself in the change of the demodulated (rectified) low-frequency acoustic pulse profile are established. It is demonstrated that parametric low-frequency radiation contains information on both absorption and scattering of high-frequency acoustic waves.