We have recently developed a new resonance theory for the scattering of compressional waves by fluid-filled spherical cavities in viscoelastic materials, and have applied it to the study of the resonance frequencies and widths of peaks in the (monopole) f0pp scattering amplitude. Using this theory, which is the viscoelastodynamical counterpart of the Breit-Wigner formalism of nuclear scattering theory, we find that (i) the relative half-width of the peaks depends linearly on the resonance frequency, (ii) the shear-absorption parameter of the viscoelastic material containing the cavity can be determined from the slope of a straight line fit to the data. This determination is possible precisely because our theory realistically accounts for absorption in the material, and thus its predictions compare favorably with experimentally measured data. Finally, the theory gives a self-consistent way to verify the weak absorption assumption inherent in the prediction. [H. Überall is also at the Physics Department, Catholic University, Washington, DC 20064, additionally supported by Code 421 of ONR.]