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

Abstract

In the present 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. In particular, 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. Note that 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 prior knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber accurately. Experimental results presented here show that although the results are sensitive to ambient temperature, a formula previously proposed by Temkin matches closely with the measured sound speed and attenuation constant. Furthermore, it is shown that the Temkin prediction accurately represents the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard, in which the sound speed is assumed to be independent of frequency.