Toward a unified formulation of the acoustic transfer admittance of cylindrical cavities for reciprocity calibration of microphones

Abstract

The pressure reciprocity technique for calibration of Laboratory Standard microphones provides the basis for primary measurement standards for sound pressure. This calibration method is described in the International Electrotechnical Commission (IEC) standard 61094-2:2009 where the key aspect relating to the calculation of the acoustic transfer admittance of couplers was recently completed and clarified in the amendment IEC 61094-2:2009/AMD1:2022. Three models are currently provided for calculating this quantity: the low-frequency solution suitable to low frequencies, the extended low-frequency solution suitable to low and medium frequencies, and the broadband solution suitable to medium and high frequencies. It is established that neither of these models is correct for all frequencies routinely considered in many National Metrology Institutes, namely from 2 Hz to 25 kHz, so that a transition must be made. Based on the fundamental equations of acoustics in thermoviscous fluid, this paper provides a unified formulation for the acoustic transfer admittance of cylindrical cavities. Under the common quasi-plane wave approximation, this paper provides a new form of solution for the Fourier equation, not restricted by any assumption on the pressure variation and leading to a new form of propagation equation in the coupler. Two techniques are used to solve the problem, the Laplace Adomian Decomposition Method and a stepped duct approximation technique. Numerical results are presented, providing substantial evidence to support the validity of these formulations. A high level of agreement is observed between the two models, approximately 10−6 dB for the amplitude and 10−4 degrees for the phase, excluding the resonance frequencies of couplers. Finally, this paper evaluates the compatibility of the extended low-frequency solution provided in the IEC amendment with the fundamental equations established in this study. A new simplified solution is provided, highlighting discrepancies in the application of the heat conduction corrective factor as compared to the guidelines outlined in the IEC amendment.