An iterative transfer matrix approach for estimating the sound speed and attenuation constant of air in a standing wave tube

Abstract

In this work, an iterative method based on the four-microphone transfer matrix approach was developed for evaluating the sound speed and attenuation constant of air within a standing wave tube. When the air inside the standing wave tube is treated as the material under test, i.e., as if it were a sample of porous material, the transfer matrix approach can be used to identify the air's acoustic properties. The wavenumber within the tube is complex owing to the formation of a visco-thermal boundary layer on the inner circumference of the tube. Starting from an assumed knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber. Experimental results presented here show that although the results are sensitive to ambient temperature, a semi-empirical formula previously proposed by Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] matches closely with the measured sound speed and attenuation constant, as does a theoretical formulation proposed by Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440–3458]. Further, it is shown that the Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] and Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440–3458] predictions accurately represent the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard [(2019). American Society for Testing and Materials], in which the sound speed is assumed to be independent of frequency.