Longitudinal stress-wave attenuation

Figure 1, The Contribution of Mode Conversion Scattering to Longitudinal Stress Wave Attenuation by Spherical Pb Inclusions in Epoxy (Attenuation = 20a log 10(e) = 8.69a)...

Attenuation occurs because the tensile release, which is traveling at an elastic longitudinal wave speed, Q, overtakes the tensile front traveling at a plastic wave speed Cp < Q. Assuming a pulse as shown in Fig. 8.10 with a stress rate in the tensile front and tensile release of a and b, respectively, an approximate analysis shows that the peak will decay by an amount... 

The material for an acoustic lens should have a low attenuation, and a high velocity to minimize aberrations. Sapphire is an excellent material in both these respects. But the high velocity has a less desirable consequence. An acoustic impedance can be defined, which is equal to the product of the velocity and the density. The impedance of sapphire for longitudinal waves travelling parallel to the c-axis is thus 44.3 Mrayl, compared with the impedance of water which at room temperature is about 1.5 Mrayl, rising to 1.525 Mrayl at 60°C. When sound is transmitted across an interface between two materials of different impedance, the stress amplitude transmission coefficient is ( 6.4.1 Auld 1973 Brekhovskikh and Godin 1990)... 

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