Abstract
SOME attempts have been made to measure the amplitude of a vibrating quartz crystal, but no method at present exists by which its absolute value in a liquid can be determined experimentally, although the amplitude can be calculated theoretically from the relation given by Vigoureux1: 
where c11 is the elastic modulus governing the thickness vibration of X-cut plate; d the change in thickness of the plate per volt (2µµm.); V the voltage applied; c1 the velocity of sound in quartz and ρc the radiation resistance of the transmission medium.
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References
Vigoureux, P., “Ultrasonics” (1950).
Wood, A. B., “A Textbook of Sound” (1955).
Parthasarathy, et al., Nature, 166, 829 (1950); Ann. Phys., 12, 8 (1953); Z. Phys., 135, 395 (1953).
Parthasarathy, S., and Narasimhan, V., Z. Phys., 143, 300 (1955).
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PARTHASARATHY, S., SINGH, H. Amplitude of a Quartz Plate vibrating in Liquids. Nature 181, 260 (1958). https://doi.org/10.1038/181260a0
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DOI: https://doi.org/10.1038/181260a0
