By Gordon S. Kino
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Additional info for Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall Signal Processing Series)
A piezoelectric transducer with a cross section of many wavelengths has very little transverse motion, so k , is the effective coupling constant. Such transducers are commonly employed in UHF applications, where the wavelengths are less than 100 pm, and often in low-frequency applications, where the wavelengths are of the order of 1 mm and the cross-sectional dimensions of the transducer are 1 or more centimeters. Similar relations hold for a shear wave transducer with a cross section of many wavelengths.
The techniques developed there are applied to propagation of waves in finite isotropic media in Chapter 2. Fortunately, in isotropic materials, it is always possible to resolve any waves present into plane shear wave and longitudinal wave components. In a finite isotropic medium, however, both types of fields are required to satisfy the boundary conditions. 1 1. (a) The correct formula for attenuation due to viscosity in water was derived by Lord Rayleigh, who showed that the result in Eqs. 28) should have q replaced by $qs,where qsis the shear viscosity of water.
9) If we eliminate T and S from Eqs. 12) where the subscripts F and B denote forward and backward propagating waves, respectively. 16) Using the boundary conditions of Eq. 2) in Eq. 11), we see that v = Sec. 17) 31 Substituting this result in Eqs. 20) zo where the parameter Zc has the dimensions force/velocity or kg/s and has the dimensions pressure/velocity or kg/m2-s. Impedances with the dimensions of force/ velocity are sometimes called radiation impedances. 18). 22) and z, = --F2 212 v(U2) Using these relations in Eq.