# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 2 Experimental Methods
An aluminum reference block of the same size as rock specimens was typically used and assumed to have zero attenuation. In this direct substitution method, the \(T_{c}\) terms can be small for aluminum and for many rocks and cancel out. The effect of diffraction loss, which was usually not corrected, can be larger; e.g., for X = 100 mm, average diffraction losses between aluminum and granite are 1.7 and 1.0 dB for the longitudinal and transverse wave attenuation (over 0.03 to 2 MHz), respectively. Thus, the correction for the diffraction loss is needed for attaining accurate measurements. In addition, the attenuation coefficients of aluminum alloys are small, but not negligible. In the earliest method for transverse wave attenuation measurements, [PERSON] and [PERSON] used quartz disk transducers in 1947 [16]. This method takes advantage of very low loss occurring in the quartz disks, although the reflection loss of 0.4 to 0.7 dB from the disk-mounted surfaces cannot be ignored. Mounting of these delicate disks is difficult and coupling repeatability was challenging, especially for the transmission arrangements. In this study, this method was used on a limited number of samples to verify the level of attenuation obtained by TDM-1 and -2. Figure 1: Schematics of attenuation experiment, including 1. direct contact test, 2. and 3. through-transmission test 1 and 2. The next approach, now called a double through-transmission method, was introduced by [PERSON] [24] in 1960, as a rotating plate method. It is a transmission method through a tilted plate sample for the velocity and attenuation measurements. This has been improved upon both from the uses of advanced analytical tools and of high-precision immersion or air-coupled test systems [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. This was used for fiber-reinforced plastics with much success for the determination of anisotropic elastic moduli. When it is used for attenuation measurements, results were sometimes vastly different from the well-established results of other methods. For example, [PERSON] [30] obtained the attenuation coefficients for longitudinal and transverse waves to be 1050 and 7500 dB/m at 2.2 MHz for polymethyl methacrylate (PMMA). The slope of the same data showed C\({}_{\rm d}\) and C\({}_{\rm dt}\) of 478 and 1740 dB/m/MHz, respectively. The C\({}_{\rm d}\) value was much higher than the other reported values on PMMA of C\({}_{\rm d}\) = 85.3 dB/m/MHz averaged from ten studies [12; 13]. Other works [31; 32; 33; 34] that relied on the double through-transmission method also reported higher attenuation values as reviewed in [12]. Thus, the double through-transmission method was suspected to suffer from the presence of unrecognized issues, such as the off-normal incidence and refraction of circular wave front [12]. However, [PERSON] et al. [35] using the same method provided significantly lower attenuation results. For PMMA, they obtained C\({}_{\rm d}\) = 101.4 dB/m/MHz and C\({}_{\rm dt}\) = 268 dB/m/MHz, averaging their 5 and 10 MHz attenuation values. These are comparable to other reported values, confirming the soundness of the double through-transmission method itself. For the transverse attenuation, [PERSON] and [PERSON] [36] obtained C\({}_{\rm dt}\) = 218 dB/m/MHz and recent interferometric measurements on PMMA gave C\({}_{\rm dt}\) = 253 dB/m/MHz (average of three slopes) [37]. These three works will be used as reference. Before embarking on a broad survey of the transverse attenuation coefficients of engineering materials of wide interest, a series of tests were conducted using PMMA as the reference material. This is to confirm that the present test methods provide results consistent with previous studies in the literature. A similar series was also performed for the case of longitudinal wave attenuation [13]. For these tests using TDM-1 and TDM-2, PMMA plates of eight different thicknesses were used, ranging from 5.25 to 27.3 mm.