The propagation of ultrasonic plane waves through a material can be expressed by a transfer function related to the attenuation and the velocity dispersion. These acoustical parameters are determined from ultrasonic spectroscopy. Experiments were performed on different polymers and for the particular materials we have tested it was observed that amorphous materials can be considered as low‐dispersive media, whereas in semicrystalline materials the velocity dispersion cannot be neglected. These experimental results are compared with those deduced from the Kramers–Kronig relations. These analytical expressions, assuming the causality conditions of every physical system, are verified for different materials proving the validity of our measurements. Other interests of the Kramers–Kronig relations are also discussed. ©1996 American Institute of Physics.