@NeffRelaxed]). Nevertheless, the set of 18 parameters introduced by Mindlin in [@Mindlin] and Eringen in [@EringenBook] is not suitable to disclose the main features of micromorphic media mainly because of unavoidable computational difficulties. We propose here to consider the relaxed micromorphic model presented in [@NeffRelaxed] which only counts 6 parameters and which, nevertheless, is fully able to describe the main characteristic features of micromorphic continua. Indeed, in [@NeffRelaxed] we showed that the linear isotropic microvoid model, the linear Cosserat model and the linear microstretch model are special cases of our relaxed micromorphic model in dislocation format. A direct identification of the coefficients gave us that the coefficient of the Cowin-Nunziato theory [@CowinNunziato], the Mindlin-Eringen theory [@Mindlin; @EringenBook] and the microstretch theory [@EringenBook; @Iesan] can be expressed in terms of our constitutive coefficients (see also [@Neff; @constants; @NeffRelaxed]). Using these identifications one could compare all the qualitative results obtained using our relaxed micromorphic model with those already available in the literature (see for instance [@Mindlin; @EringenBook; @Ghiba; @Ghiba1; @Ghiba2; @Ghiba3; @Ghiba4; @Ghiba5; @Ghiba6] and references therein) concerning classical theories of elastic materials with microstructure.

By studying dispersion relations in the proposed relaxed model, we show that wave propagation in such simplified 