K. Hou and J.S. Bolton, "A Transfer Matrix Method for Estimating the Dispersion and Attenuation of Plane Waves in a Standing Wave Tube," 157th meeting of the Acoustical Society of America, Paper No. 2pEAa10, Portland, Oregon, May 2009. Abstract published in the Journal of the Acoustical Society of America, 125, 2596, 2009.


In this paper, an iterative method is described for evaluating the frequency-dependent sound speed and attenuation constant of plane waves propagating in a standing wave tube. The dispersion in this case results from the existence of a visco-thermal boundary layer at the internal surface of the tube. The procedure is based on the four-microphone transfer matrix method for measuring the transmission loss of acoustical materials. In the latter procedure, a sample is placed between two pairs of microphones and is exposed to an incident plane wave field. In the present case, a finite length air column within the standing wave tube is treated as the sample material. Since knowledge of the dispersion characteristics of plane waves within the tube is required to perform this measurement, an iterative method must be applied during post-processing to estimate the complex wave numbers in the sample section. The measured results were found to be in good agreement with the semi-empirical Temkin formula for sound wave attenuation in tubes. The experimental results also showed that the air temperature within the tube has a significant impact on the results. The temperature can be estimated by adjusting it to find the optimal agreement with the Temkin predictions.


Transfer Matrix Method, Standing Wave Tube, Sound Speed, Phase Speed


Acoustics and Noise Control

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