Acoustic pulse propagation in a medium with two relaxation processes. Analysis of the exact solution

On the basis of the Efros theorem on the generalized convolution, a new ana lytical representation of the Green's function is obtained for an acoustic pulse propagating in a medium with two relaxation processes. This represent ation contains three parts which describe, respectively, the acoustic precu rsor and the high- and low-frequency components of the pulse body. The high -frequency part of the pulse body may be written in the invariant form that is valid for any relaxation time spectrum (RTS). The low-frequency part of the pulse body exhibits a much more complicated dependence on the paramete rs of the RTS. This dependence is analyzed and some analytical expressions for its calculation are obtained. The validity of these expressions is conf irmed by the comparison with the results of direct numerical calculations.