Measuring elastic constants (Cij) of composite materials from ultrasonic velocities is a very well known technique1,2, using the propagation of bulk modes generated at the fluid-solid interface. There is still a question about the validity of these measurements at lower frequencies or for static stress fields. These materials made with viscoelastic matrix are anisotropic and viscoelastic. Hence, the attenuation is also anisotropic. In an absorbing medium, the propagation of waves is dispersive: the phase velocity depends on the frequency. Attenuation and velocity are linked together through the Kramers-Kronig relations that are deduced from the principle of causality3.