## 1 Introduction  
Non-destructive evaluation (NDE) methods based on stress wave propagation have contributed to quality assurance and failure prevention in many industries [1; 2; 3]. The methods include ultrasonic testing (UT), which uses active interrogation of target components, and acoustic emission (AE) testing, which relies primarily on \"acoustic\" signals emitted from the target. In recent years, their roles have expanded into continual monitoring and preventive maintenance of wide-ranging products and infrastructures, offering useful tools for structural health monitoring [4; 5; 6; 7]. As the size of structures being inspected increases, the attenuation of stress waves becomes a concern, especially for components of modern fiber-reinforced composites and other high damping materials. In a preceding report [7], a section was devoted to collecting available data on structural alloys, polymers, and fiber-reinforced composites. Despite long-standing scientific and engineering interests in this subject going back to the work of [PERSON] and [PERSON] in the 1940s [8], available ultrasonic attenuation data were found to be limited. Most of the attenuation values collected in [7] were for longitudinal waves, while the data for transverse waves were even more sparse, lacking an adequate theoretical foundation, as appropriate diffraction correction has been unavailable. As data from some reports were given as ranges in [7], the total tabulated data count exceeded 80, but this number was still less than 200 for only about 40 different types of materials. Most polymer data, with about 50 being available in [9; 10; 11], were not included, in part because the test frequency was in the low kHz region or below and was often unidentified. Technical standards for their measurements and validation were also inadequate [12; 13]. In order to fill the gap in the presently inadequate database, a study was initiated examining experimental techniques and which culminated with a comprehensive report. [PERSON] [14; 15] provided a thorough review of this subject and application examples of a buffer rod method, which he and his colleagues had developed earlier [16]. Their method and its variations have been used by many works cited in [7], including ASTM Standard C1332 [12], as well as in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. [PERSON] et al. [27] published a tutorial for another approach for attenuation measurement, namely the immersion methods. While these methods require advanced ultrasonic instrumentation capable of precise sensor-sample alignment, water coupling allows the inspection of curved surfaces of engineering components. [PERSON] and his coworkers [28; 29; 30; 31] applied the methods to detect the hard inclusions in aerospace Ti alloys and to evaluate the cleanliness of steel samples. Here, it is necessary to define terms that will be used, as wave attenuation is characterized using several different parameters. Attenuation coefficient \(\alpha\) is often used in UT and AE to represent an exponential decay. Taking the initial and attenuated wave amplitude in the displacement, \(\mathrm{A_{o}}\) and \(\mathrm{A_{r}}\) and the propagation distance, \(\mathrm{x}\), we have  
\[\mathrm{A}=\mathrm{A_{o}}\exp{(-\alpha\;x)}. \tag{1}\]  
The commonly used unit for \(\alpha\) is dB/m. However, it is sometimes convenient to use Np/m, whereby 8.686 dB = 1 Np. Np stands for Neper, a non-dimensional unit that is useful in numerical computation. In this work, only longitudinal waves are considered and no subscript is used for wave types. Previously in [7], \(\alpha\) was denoted by \(\alpha_{\mathrm{p}}\). This \(\alpha\) is related to the damping (or loss) factor \(\eta\) by \(\eta=\alpha\lambda/\pi\), where \(\lambda\) is the wave length and \(\alpha\) is given in the unit of Np/m.