Numerical calculation of the phase of the complex acoustic impedance of air in a cylindrical closed volume

As a result of primary pressure calibration (by reciprocity technique or by pistonphone method) of LS-type microphones, their corresponding complex sensitivity is determined. However, one of the problems of this procedure is the need to theoretically determine the complex acoustic impedance of air enclosed in a closed volume. As experiments and various theoretical works have shown for almost 100 years of studying the above-mentioned problem, the adiabatic approximation of acoustic oscillations, adopted at the beginning, is not correct. The most signifi cant (in the fi rst approximation) infl uencing factors, due to which the adiabatic approximation alone is not correct, are the heat exchange of air inside a closed volume with the external environment (through the walls of a closed volume) and refl ected waves that appear at high frequencies (as the length of the closed volume and the wavelength of oscillations are compared). Numerical simulation is proposed to study these factors. The numerical algorithm is based on the regularized NavierStokes equations with quasi-gas-dynamic approach, taking into account viscosity, thermal conductivity and compressibility of air. In this paper, the phase of the complex acoustic impedance of air in a closed volume with heat-conducting and heat-insulated walls is determined. The results of the study are relevant both for calibration of measurement microphones at low and infrasound frequencies by the pressure reciprocity technique and the pistonphone method, and for studying acoustic processes in liquid and gaseous media using numerical modeling. Measurement devices that was transmitted the unit of sound pressure in the air from measurement microphones calibrated by the primary method are used, for example, when monitoring noise from various sources (industrial activity, transport), 

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