Transducer Measurements by Electrical Impedance

Separation of the complex quantities into real and imaginary parts yields 

A warning should be added that because of the small amplitudes of motion in the sample there is a risk of falsification by small vibrations or lack of complete rigidity in the apparatus itself. Careful design and tests with materials of known properties can eliminate this danger. 

DYNAMIC (OSOLLATORY) MEASUREMENTS OF CHARACTERISTIC IMPEDANCE ( SURFACE LOADING ) 

The density p enters because the inertia of the sample plays an essential role in the wave propagation. For a purely viscous liquid, 31m Xm and r]o = 231m jutp. The total mechanical impedance Rm + iXm is (3tM + i Xm) times the area of contact A plus the contributions from whatever inertia, elastance, and frictance must be attributed to the apparatus itself. 

Most characteristic impedance devices are operated near a system resonance to achieve high sensitivity. This feature has the disadvantage that measurements can be made only at a single frequency, or a few discrete frequencies, instead of the continuously variable frequency range provided by the methods of the preceding sections. However, only such devices have provided measurements on viscoelastic liquids with very low viscosity and rigidity. 

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