Estimation and minimization of errors caused by sample size effect in the measurement of the normal absorption coefficient of a locally reactive surface

In this paper the effects of the finite size of a sample on the measurement of the normal absorption coefficient are explored with the aid of a BEM model. Both the experimental method and BEM simulations assumed free-field conditions and are based on the measurement of pressure and particle velocity at the same point. They will be referred to herein as the PU method. Before exploring the BEM model, measurements were performed in a semi-anechoic room for experimental validation. A direct comparison of the BEM model and experimental data does not appear to have been presented elsewhere, at least under the conditions presented herein. This validation may help to improve confidence in the PU experimental technique and the use of the BEM as a tool to enhance the quality of experiments. After experimental validation the measurement parameters are varied in the BEM model in order to investigate their effect on the measurement and to find strategies to minimize the error induced by the sample size effect. The strategies found with use of BEM simulations were also tested experimentally in order to test its validity. Recommendations for improved precision in the measurement of finite samples are given at the end of this paper.

[1]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[2]  E. Williams,et al.  Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography , 1999 .

[3]  Yasuhito Kawai,et al.  Estimation of the area effect of sound absorbent surfaces by using a boundary integral equation , 2002 .

[4]  Emiel Tijs,et al.  In Situ PU Surface Impedance Measurements for Quality Control at the End of an Assembly Line , 2009 .

[5]  Kunikazu Hirosawa,et al.  Investigation of absorption coefficient measurement of acoustical materials by boundary element method using particle velocity and sound pressure sensor in free field , 2009 .

[6]  Murray Hodgson,et al.  Use of pseudo-random sequences and a single microphone to measure surface impedance at oblique incidence , 1997 .

[7]  Kenneth E. Gilbert,et al.  An exact Laplace transform formulation for a point source above a ground surface , 1993 .

[8]  Kazuhiro Takashima,et al.  Comparison of three measurement techniques for the normal absorption coefficient of sound absorbing materials in the free field. , 2009, The Journal of the Acoustical Society of America.

[9]  Toru Otsuru,et al.  Ensemble averaged surface normal impedance of material using an in-situ technique: preliminary study using boundary element method. , 2009, The Journal of the Acoustical Society of America.

[10]  Yvan Champoux,et al.  New empirical equations for sound propagation in rigid frame fibrous materials , 1992 .

[11]  E. N. Bazley,et al.  Acoustical properties of fibrous absorbent materials , 1970 .

[12]  Sven‐Ingvar Thomasson.  Reflection of waves from a point source by an impedance boundary , 1976 .

[13]  Jean François Allard,et al.  Measurements of acoustic impedance in a free field with two microphones and a spectrum analyzer , 1985 .

[14]  Emiel Tijs,et al.  A Comparison of Three Methods to Calculate the Surface Impedance and Absorption Coefficient from Measurements Under Free Field or in situ Conditions , 2011 .

[15]  Kohei Yamamoto,et al.  The required sample size in measuring oblique incidence absorption coefficient Experimental study , 2001 .

[16]  U. Ingard.  On the Reflection of a Spherical Sound Wave from an Infinite Plane , 1951 .

[17]  Eric Brandão Carneiro.  Análise teórica e experimental do processo de medição in situ da impedância acústica , 2012 .

[18]  Gerrit Vermeir,et al.  Measuring the free field acoustic impedance and absorption coefficient of sound absorbing materials with a combined particle velocity-pressure sensor , 2006 .