Reflexion of shear waves

Though this experiment deals with a particularly simple situation, the basic principle that it illustrates is relevant to the discussions that follow on hydrodynamic instability ( 3.11). 

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. 

Now the velocities associated with the incident, reflected and transmitted waves may be written as 

Since according to (3.7.4) the real and imaginary parts of Z are of equal magnitude, it follows that 

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