Ultrasonic wave reflection coefficient

The impedance is practically important because it determines the proportion of an ultrasonic wave which is reflected from a boundary between materials. When a plane ultrasonic wave is incident on a plane interface between two materials of different acoustic impedance it is partly reflected and partly transmitted (Figure 3). The ratios of the amplitudes of the transmitted (At) and reflected (Ar) waves to that of the incident wave (Aj) are called the transmission (T) and reflection coefficients (R), respectively. 

The subscripts 1 and 2 refer to the material the wave travels in and the material that is reflected by or transmitted into, respectively. These equations show that the maximum transmission of ultrasound occurs when the impedances and Z2 of the two materials are identical. The materials are then said to be acoustically matched. If the materials have very different impedances, then most of the US is reflected. The reflection and transmission of ultrasound at boundaries has important implications on the design of ultrasonic experiments and the interpretation of their results. In addition, measurements of the reflection coefficient are often used to calculate the impedance of a material. 

ANL s ultrasonic viscometer is a nonintrusive in-line device that measures both fluid density and viscosity. The design of the viscometer is based on a technique that measures acoustic and shear impedance. The technique was first applied by Moore and McSkimin (1970) to measure dynamic shear properties of solvents and polystyrene solutions. The reflections of incident ultrasonic shear (1-10 MHz) and longitudinal waves (1 MHz), launched toward the surfaces of two transducer wedges that are in contact with the fluid, are measured. The reflection coefficients, along with the speed of sound in the fluid, are used to calculate fluid density and viscosity. Oblique incidence was commonly used because of better sensitivity, but mode-converted waves often occur in wedges that do not exhibit perfect crystal structure and lack well-polished surfaces. For practical applications, we use the normal-incidence arrangement. 

Lowe, M. and Cawley, R, Comparison of reflection coefficient minima with dispersion curves for ultrasonic waves in embedded layers. Rev. Prog. Quant. Nondestruct. Eval., 14B, 1505-1512(1995). 

The viscosity coefficients may also be determined by studying the reflexion of ultrasonic shear waves at a solid-nematic interface. The technique was developed by Martinoty and Candau. A thin film of a nematic liquid crystal is taken on the surface of a fused quartz rod with obliquely cut ends (fig. 3.7.1). A quartz crystal bonded to one of the ends generates a transverse wave. At the solid-nematic interface there is a transmitted wave, which is rapidly attenuated, and a reflected wave which is received at the other end by a second quartz crystal. The reflexion coefficient, obtained by measuring the amplitudes of reflexion with and without the nematic sample, directly yields the effective coefficient of viscosity. 

Determination of the viscosity coefficients from the mechanical wave propagation and attenuation in the ordered nonatic phase is probably the closest to the first principles methods. The shear impedance technique is based on measuring the reflection and attenuation of ultrasonic shear waves [90-92]. The conqtlex shear impedance of the nematic sample, Zn = Rn + iXn, is determined from the complex... 

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