A Comparison of Three Methods to Calculate the Surface Impedance and Absorption Coefficient from Measurements Under Free Field or in situ Conditions

Abstract

In this paper the measurement, in situ or under free-field conditions, of the surface impedance and absorption coefficient is investigated. Numerical simulations of the measurement of impedance above al ocally reactive surface is performed with the Boundary Element Method (BEM). Experiments are also made in asemi-anechoic chamber and in ar egular office room. Three calculation methods used to obtain the surface impedance of an absorbent surface are described and compared, twoo ft hem being iterative.T he first, referred to herein as the "q-term", relies on an exact description of the sound field above an infinite locally-reactive plane. The second, the "F-term", relies on an approximation for large values of the argument k | r 2 | in its equations. The third, the "Plane Wave Approximation (PWA )",isasimplification of the spherical wave reflection which considers that the reflected wave has its amplitude and phase changed by asimple planar reflection coefficient. The "F-term" and the "Plane Wave Approximation" methods also assume an infinite locally-reactive plane. The three calculation methods are compared, the differences in the found results are discussed. The three methods are compared mainly for small sound-source to sensor distances (| r 2 | = 0.3m)and it is seen that theytend to convergeasthis distance increase. This comparison is relevant to in situ impedance measurements, since abad choice of the calculation method may lead to apoor result. PACS no. 43.58.Bh, 43.20.El, 43.55.Ev Received2May 2011, accepted 18 September 2011.the sound pressure at twol ocations close to the surface of the absorber.T he particle velocity wasc alculated by the gradient of the sound pressure. The authors assumed the acoustic field to be formed by plane waves. The in situ measurements were compared with impedance tube results. Substantial deviation wasf ound below5 00 Hz, which can be attributed to an insufficient spacing between the microphones and to the assumption of plane waves. Li and Hodgson [2] also used twom icrophones, assuming that the reflected spherical wave fronts have its amplitude and phase changed by aplanar reflection coefficient. Despite the assumption regarding the reflection, asurface impedance closer to that obtained with the phenomenological model wasestimated. The results in reference [2] were compared with those in reference [1]. The assumption in reference [2] is the same as that described in section 3.3.Ac ommon weakness of these methods is the lack of a good description of the sound field above the surface. The ©S.Hirzel Verlag · EAA 1025 ACTA ACUSTICA UNITED WITH ACUSTICA Brandão et al.:M easurement of free field surface impedance Vol. 97 (2011)

Measuring Sound Absorption: Considerations on the Measurement of the Active Acoustic Power

“…It will be referred to as the reference model hereafter.An umber of methods [5,6,7,8] assume plane wave incidence, whereas other methods consider spherical wave incidence [9,10,11,12,13,14,15,16]. Adifferent approach is applied in the in situ method by Takahashi et al [7], further studied by Otsuru [17], and Din [8].…”

“…Possible causes are multiple, for instance non-omnidirectionally radiating sound sources, samples that are non-locally reacting, or samples having an onplanar surface. Fitting the reference model parameters to the measurement results will then typically lead to sound absorption coefficients that are inaccurate to ag reater or lesser extent [14,19].…”

Study and development of an in situ acoustic absorption measurement method

“…In some cases, similar values are found [27,110,115], [125]. However, discrepancies are found in other cases that cannot be explained by near field effects only.…”

“…Such similarities of both models were also reported in [74], [114], which is remarkable because the fundamentals of both models are rather different. However, discrepancies can be found as was also stated in [115]. This is apparent for the Linoleum sample for which the Q-term results are unreliable (orange line).…”

“…The discrepancies that can be found with the aforementioned models are discussed in this chapter. Results and conclusions are partially based on those reported in [73], [114], and [115].…”