Length error analysis for impedance tube measurements

Abstract

Length error analysis of the transfer function method and improved standing wave ratio (SWR) method for impedance tube measurements is presented in this letter. The error of measuring the complex reflection coefficients R is caused by errors in measuring the positions of the two microphones (or the two pressure points for the improved SWR method). Results agree with Abom and Boden’s [J. Acoust. Soc. Am. 83, 2429–2438 (1988)] conclusions, i.e., errors will be large if s, the separation distance of the two microphones, is about one-half wavelength and will be small if s is about one-quarter wavelength. Results also show that in order to reduce the amplitude error of R, it is better to locate one microphone near a minimum pressure point and the other near the adjacent maximum pressure point. To reduce the phase error of R for the transfer function method, preference of the two microphone locations depends on the combination of length errors Δl1 and Δl2. Phase error reduction for the improved SWR method requires an accurate measurement of the minimum pressure point.