Acoustic coupling between resonator tubes in quartz-enhanced photoacoustic spectrophones employing a large prong spacing tuning fork

Abstract

A theoretical model describing the acoustic coupling between two resonator tubes in spectrophones exploiting custom-made quartz tuning forks (QTFs) is proposed. The model is based on an open-end correction to predict the optimal tube length. A calculation of the sound field distribution from one tube exit allowed for the estimation of the optimal radius as a function of the QTF prong spacing and the sound wavelength. The theoretical predictions have been confirmed using experimental studies employing a custom QTF with a fundamental flexural mode resonance frequency of 15.8 kHz and a quality factor of 15,000 at atmospheric pressure. The spacing between the two prongs was 1.5 mm. Spectrophones mounting this QTF were implemented for the quartz-enhanced photoacoustic detection of water vapor in air in the mid-infrared spectral range.