A Determination of Some of the Properties of the Piezo-Electric Quartz Resonator

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Abstract
Entirely consistent determinations of the logarithmic decrement of X-cut quartz rods whose natural frequencies are of the order of seventy kilocycles have been obtained during the last few years. The decrement is obtained from measurements on oscillographic records of the decay of the free vibrations of the resonator. The most extreme (lowest) values of decrement have been checked by an entirely independent method; namely, by tracing the resonance curve, the agreement between the two methods being to within a few per cent. Extended studies by the former method have shown the logarithmic decrement to be a linear function of the pressure of the surrounding gas, and the energy losses in the two gases tried, air and hydrogen, to be in the ratio of their radiation resistances. This assumes previous elimination of mounting losses, which for ordinary mountings are even larger than radiation losses. When radiation losses have been eliminated, the effect of the abrasive used in making the usual ground finish of the surfaces of the quartz becomes obvious, the lowest decrements being obtained when the surfaces have been etched. Representative decrements measured under various conditions are as follows, the corresponding reactanceresistance-ratio Q being inserted in parentheses following each logarithmic decrement. Ground surfaces, in air at atmospheric pressure, 126×10-6(25,000) Ground surfaces, in hydrogen at atmospheric pressure, 31×10-6(101,000) Ground surfaces, in vacuum, 11-17×10-6(290,000-180,000) Etched surfaces, in vacuum, 6.4×10-6(490,000) Etched surfaces, polished, in vacuum, 5.

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