## 5 Summary  
This study determined attenuation characteristics of numerous engineering materials, encompassing metals, ceramics, polymers, fiber-reinforced composites, wood, and rocks. Attenuation measurements utilized two methods, named transmission difference methods 1 and 2 (TDM-1 and TDM-2), which included corrections for diffraction effects and the transmission coefficient. The latter term was unnecessary with TDM-1, which was used to obtain the actual correction constant for TDM-2. These two methods usually produced attenuation data with 12% or better agreement and were verified using PMMA to match the averaged attenuation coefficient from the literature. Attenuation behavior was determined over broadband spectra, extending up to 15 MHz in low attenuating materials. Over 300 tests were conducted and attenuation results are given in tabular form. The results are compared to published data when available. Various findings are summarized below. (1) The attenuation spectra were characterized in combination with four power law terms, with many showing linear frequency dependence with or without Rayleigh scattering. This combined spectrum is called the Mason-McSkimin relation, named after the authors who first discovered it. The linear term comes from hysteretic damping, which has long been neglected in metal studies. A dislocation bow-out was proposed to explain the linear term for metals, but its physical basis requires additional investigation. Koehler-Granato-Lucke theory may account for some quadratic frequency dependencies, but their limited observations mean this explanation is unconvincing. Further, quadratic and cubic dependencies due to Datta-Kinra scattering and Biwa scattering, respectively, were used for some materials to appraise attenuation mechanisms. The Datta-Kinra quadratic dependence is due to multiple scattering of distributed scattering centers, while the Biwa cubic dependence comes from scattering due to parallel fibers. (2) Transmission difference methods were used for attenuation measurements. A correction procedure for transmission coefficients was introduced. From many test results, some previously unknown behaviors emerged upon data evaluation. The effects of cold working, tempering, and annealing were complex and sometimes contradictory. Comparison with available literature was attempted for some, but usually prior data were unavailable. This collection of new attenuation data will be of value in selection of materials and in designing structural health monitoring and non-destructive inspection protocols. Summary comments on various types of materials are given below. (3) Most structural steels exhibited low to medium attenuation coefficients. Linear frequency spectra were common with the Mason-McSkimin relation for one-quarter of samples tested, consisting of ferritic-pearlitic low-C steels and austenitic stainless steels. Cold working (CW) and phase transformation imposed vast changes in \(\alpha\) values, with two contradictory CW effects--type-p and type-n; that is, CW increased or decreased \(\alpha\) values. Martensitic and bainitic transformation products also responded differently to tempering. (4) Most non-ferrous metallic materials also exhibited the linear frequency spectra or Mason-McSkimin relation. The levels of attenuation were low in Al and Mg, but most others were comparable to typical ferrous alloys. Two cold-worked plates showed anisotropic behavior with quadratic frequency spectra in the in-plane orientations. Such unusual spectra, which are probably a form of dislocation damping, are expected to vanish with annealing if they follow the trend found for low-C steel. Other anisotropic attenuation was found and appeared to result from mechanical processing steps, since the thickness direction typically showed higher attenuation. This behavior appears to be previously unknown. (5) Cast iron behavior was grouped into two main types.