Standing wave apparatus for measuring fundamental properties of acoustic materials in air

Abstract

A standing wave apparatus employing multiple microphones for measuring fundamental properties of acoustic materials is analyzed. The apparatus is basically a tube with a compression driver at one end with a rigid plug at the other and a finite length sample of acoustic material strategically located in between. A microphone array is then used in obtaining the pressure and velocity boundary conditions of the sample from which basic acoustic properties can be calculated. Such properties as internal propagation constant, characteristic admittance (inverse impedance), and bulk modulus are measured and data for a 100-pore-per-inch (ppi) open-cell acoustic foam is presented. A relatively new parameter called the complex flow impedance is measured under low-and high-intensity levels and is shown to exhibit finite amplitude properties. Of particular concern is how finite sample lengths effect the accuracy of the measurements. It is shown that in general a long sample length (on the order of a wavelength or more) is required for the accurate measurement of propagation constant, characteristic admittance, and bulk modulus measurements while a short length (much less than a wavelength) is required for good finite amplitude flow impedance measurements. Previous studies of flow impedance have been carried out using a similar but not identical apparatus [W. E. Zorumski and T. L. Parrott, "Nonlinear AcousticTheory for Rigid Porous Materials," U.S. NASA TN-6196, 1971; K. U. Ingard and T. A. Dear, "Measurements of the Acoustic Flow Resistance," J. Sound Vib. 103, 567-572 (1985) ]. However, the previous studies have lacked an analysis of the possible errors in the measurement methods that can be very significant for these types of flow impedance measurements. PACS numbers' 43.25.Ed, 43.25.Zx, 43.85.Bh LIST OF SYMBOLS a• effective pore radius in rigid frame model Zz. d sample thickness Zs, , kb complex propagation constant of wave in porous material ]•b K complex bulk modulus of fluid in porous material M mass loading part of flow impedance, = I'm(Zr)/cø Po static pressure of fluid Pb P complex excess (acoustic) pressure amplitude (taken to be the peak value, not rms) Po Npr Prandtl number of fluid rrø R resistive part of flow impedance, = Re(Z•.) v U complex particle velocity (the peak value, co not rms) COT

Measurement of Heat Flow Transmitted through a Stacked-Screen Regenerator of Thermoacoustic Engine

“…This result indicates that r 0 should be used instead of r eff for better estimation of heat flow. Other earlier studies [29,31] have demonstrated that two effective radii are necessary to explain the viscous behavior and the thermal behavior in tortuous porous media because the viscous effects are governed by narrower regions of the channel, whereas the thermal effects are determined by wider regions [32,33]. Our experimentally obtained results provide another example representing the need of the effective thermal radius, in addition to the effective viscous radius.…”

“…Thermoacoustic theory describes that the flow resistance of the regular flow channel is a constant [17][18][19], independent of the velocity amplitude, whereas that in the porous media with tortuous flow channels is shown to increase with the velocity [28][29][30] or Reynolds number [2][3][4][5]7]. From measurements of the acoustic field, we have proposed modification of the effective radius r 0 to have velocity dependence [16] as…”

Static flow resistivity measurements based on the ISO 10534.2 standard impedance tube

“…It was clear that the IngardeDear method [7,8], the McIntosh method [9], and the Doutres method [13] are not practical because one microphone needs to be installed at the rigid termination of the impedance tube. The ReneJacobsen method [10] is also difficult to perform as the specimen needs to be placed between two measuring microphones.…”

“…Ingard and Dear [7,8], McIntosh et al [9] and Ren and Jacobsen [10] proposed to measure the sound pressure at both sides of the test specimen, and divided the sound pressure drop by the flow velocity and the specimen thickness to calculate the static flow resistivity. Woodcock et al [11] measured the propagation constant and the characteristic impedance of the material by adopting the two-cavity [14] and two-thickness [15] methods, and then calculated the effective flow resistivity using the inverse equation of the Delany and Bazley empirical formulae [16].…”

Numerical and analytical solutions for sound propagation and absorption in porous media at high sound pressure levels

“…11 The sound propagation and absorption properties of porous media under high sound pressure level conditions have been studied by a number of authors. [12][13][14][15][16][17][18][19][20] Zorumski and Parrott 12 introduced the concept of temporal impedance, which contains resistance and reactance, in their theoretical and experimental studies on the acoustic nonlinearity in rigid porous materials. The instantaneous resistance of rigid porous materials was found to be independent of the testing frequency and equal to the flow resistance of the materials, and the instantaneous reactance is a function of the acoustic fluid velocity.…”