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By means of the clamped-free bar model, the impedance change of the tuning fork-type quartz resonator by the acoustic radiation resistance and the Stokes' resistance is studied theoretically and experimentally. From the analysis, it is found that the impedance change due to the acoustic radiation resistance and to the Stokes' resistance depends strongly on the shape of the resonator. It is found also that the impedance change by the acoustic radiation resistance cannot be neglected at the atmospheric pressure.

By using the clamped-free bar model, the impedance change of the tuning fork-type quartz resonator due to gas pressure was studied theoretically and experimentally. The drag force by the gas-kinetics and the mechanical loss energy caused on the crystal surface by the viscous friction are equated to the electric loss energy in the crystal resonator so that a new theoretical equation for the pressure-impedance characteristic was derived. The size dependence of the impedance change was derived theoretically and verified.