A reconstruction algorithm that synthesizes the relaxation attenuation spectrum in a wide frequency range is presented. And the effective relaxation time of gas can be estimated by two approaches, which are base on SSH theory and experimental data, respectively. The acoustic attenuation spectra of various polyatomic gas mixtures, consisting of nitrogen, methane, oxygen, carbon dioxide and water, were estimated by the reconstruction algorithm. The sound frequency rang of interest is from 1 Hz to 10 GHz. Comparing with the results of the relaxation attenuation based on the DL model, the estimations of relaxation attenuation of the reconstruction algorithm agreed with the latter. The precision of the reconstruction algorithm depends upon the knowledge of the physical mechanism of molecular relaxation processes. In addition, the reconstruction algorithm was applied to quantitatively determining the concentrations of water and carbon dioxide in some polyatomic gas mixtures. The results show that the relaxation attenuation can be used as a quantitative probe of the composition of polyatomic gas mixtures. And this could lead to the development of smart acoustic gas sensors capable of determining the precise compositions of gas mixtures.