Impedance measurements on reflective surfaces: effect of nodes

The ISO 13472-2 standardizes the in-situ measurement of normal-incidence acoustic absorption of road pavements. The standard describes the use of the two-microphone method with an impedance tube specially configured for sealing against pavement surfaces. The method is of interest to the tire-pavement noise and vehicle pass-by noise communities. For roads constructed of dense graded asphalt, for example, pass-by noise test tracks conforming to ISO 10844, the pavement is a highly reflective surface. Under this measurement condition, the acoustic field within the tube develops nodes at one or the other microphone positions at characteristic frequencies. These nodes present as sharp peaks and valleys in the two-microphone transfer function. Such narrow bandwidth features are susceptible to measurement error, in particular, signal processing leakage as evidenced by significant drops in the coherence function at the frequencies of the nodes. In this paper we study the nature of the nodes and the effect they have on the two-microphone transfer function and coherence function. We further investigate how different formulations of the transfer function affect the overall 1/3rd octave band accuracy. The effect of the number of averages on both coherence and leakage error is assessed. The potential to solve this leakage effect by switching microphones to other positions is evaluated in relation to a procedure with two fixed microphones. It was concluded that although shifting microphone positions does have advantages in terms of preventing leakage, the mandatory application of a reference measurement reduces the overall error. Finally, recommendations for improving the procedure in ISO 13472-2 are formulated.