MECHANICAL rUOl'lORTIlOS OF POLYMERS 



133 



rod by means of a Y-cut or AT cut crystals soldered to a silver paste 

 layer baked on the fused quartz surface. The particle motion of the 

 shear wave is parallel to the large reflecting surface and hence only 

 shear waves are reflected from this surface. These impinge on a sec^ond 

 shear crystal which is connected to an amplifier and oscillograph. Since 

 the attenuation in fused quartz is so low, a long series of reflected pulses 

 appear on the oscillograph. When a liquid, whose shear properties are 

 to be measured, is placed on the fused ciuartz surface, this causes a 

 change in the amplitude and phase of the reflected wave. By using the 

 balance method shown by Fig. 7, in which two identical fused quartz 

 rods are used, one of which has a liquid layer and the other does not, 

 and by using a phase shifting network and an attenuator to balance out 



TO PULSED 

 OSCILLATOR 



TO 

 AMPLIFIER 



Fig. 7 — Method for obtaining resistance and reactance terms for high fre- 

 cjuency shear reflection method. 



pulses, the shear impedance of the liquid can be determined. If R is the 

 loss per reflection expressed as a current ratio, 6 the change in phase 

 angle recjuired to rebalance the circuit and (p the angle between the wave 

 normal and the reflecting surface, it can be shown* that the shear im- 

 pedance of the liquid is 



Z M = R\i -\- jX M — Zq cos (p 



"1 - R'' + 2jR sin 6 



.1 + 7^2 _f_ 2R cos d_ 



(7) 



where Zq is the impedance pv for shear waves in the quartz. This is 

 equal to 



Zq = 2.20 X 3.76 X 10^ = 8.27 X lO' mechanical ohms 



Since this impedance is much larger than that of the liquids that are to 

 be measured, the .sensitivity is increased by making (p large. In practice 

 (f was taken as 80°. This method is applicable from 3 mc up to 100 mc 



