Model calculations for ultrasonic plate - liquid - plate resonators: peak frequency shift by liquid density and velocity variations

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Abstract
Ultrasonic resonators - consisting of the liquid sample, enclosed by two planar piezoelectric transducer plates - permit a direct and accurate determination of liquid sound velocities at kilohertz and megahertz frequencies. Such plate - liquid - plate (PLP) resonators offer a resolution , which is important for analytical work in chemistry, bio- and physico-chemistry and for some technical applications. A simple one-dimensional resonator model is derived which permits calculation of the spectrum of the longitudinal (nonharmonic) eigenfrequencies (n = 1, 2, 3, 4 ...) as a function of liquid and resonator parameters. This model obtains the peak shift by variation of liquid velocity and density as well for plane wave propagation; the effect from variations in has been neglected in most ultrasonic studies so far. Caused by a frequency-dependent phase shift for sound reflection at both liquid/transducer interfaces, the differential quotients and of the `real' resonator deviate from those of an `ideal' PLP resonator with perfect, `hard' reflection (reflection factor ) and harmonic overtones ( is the liquid fundamental frequeny; one half liquid wavelength equals transducer separation x). The figures show typical acoustic impedance and admittance spectra, which are calculated for a model configuration; they illustrate features of the harmonic numbers in the liquid cavity and longitudinal mode counting. Equations are given for the dimensionless, normalized differential quotients and . Plots demonstrate systematic aberrations from `ideal' resonator behaviour, which can affect high-precision sound velocity measurements.