132 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



re-balance the circuit. These are measured by the amount of attenuation 

 in nepers (1 neper = 8.68 db) and the number of radians phase shift 

 required to re-establish a balance. An alternate method of measuring 

 phase shift is to measure the change in frequency required to re-estab- 

 hsh balance. If this method is used the phase shift change of the overall 

 circuit with frequency has to be calibrated for the uncovered rod by 



^^LIQUID 



^v SOLDERED ,' 

 "~ JOINTS- 



Fig. 6 — High frequency shear reflection method for measuring shear imped- 

 ances of liquids. 



noting the frequencies for which 360° phase shifts (as measured by 

 balance) occur in the circuit. 



It is shown in the appendix that the torsional impedance of the 

 liquid per square centimeter is given by 



where p is the density, and Wo the sound velocity in the rod, a is the 

 radius and I the covered length of the rod and A^ and LB are respec- 

 tively the change in attenuation in nepers and the change in phase shift 

 in radians to re-establish balance. If a very viscous liquid is used it may 

 be necessary to correct for the fact that the torsional impedance may 

 differ from the plane wave impedance as discussed in the appendix. 



This device can measure liquids having dynamic viscosities from 10 

 poise to 1,000 poise with an accuracy of the order of 10 per cent. The 

 frequency range covered may be from 20 to 200 kc depending on the 

 size of the crystal used to drive the rod. Hence it supplements the 

 torsional crystal method for very viscous liquids. 



At frequencies above 500 kc, the torsional crystal becomes too small 

 to be used practically and recourse is had to a high frequency pulsing 

 method.* As shown by Fig. 6, shear waves are set up in a fused quartz 



8 W. P. Mason, W. O. Baker, H. J. McSkimin and J. H. Heiss, "Measurements 

 of the Shear Elasticity and Viscosity of Liquids bv Means of Ultrasonic Shear 

 Waves," Phys. Rev., 75, No. 6, March 15, 1949, pp. 936-946. See also H. T. O'Neil, 

 "Refraction and Reflection of Plane Shear Waves in Viscoelastic Media," Phys. 

 Rev., 75, No. 6, March 15, 1949, pp. 928-936. 



