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In this paper, a new acoustic lumped element-based method to measure the complex density of porous materials at low frequency is provided. Based on the electroacoustic analogy of wave propagation inside a porous medium, an analytical derivation of the measurement method is given. Measurements can be performed in a short open tube and by placing the tested sample between an acoustic source (i.e., a loudspeaker) and the open-end section by using two microphones. To validate the methodology, different typologies of porous materials, characterized by different values of the complex wave number k ̃ and thickness d, have been tested. The proposed method provides accurate and reliable results when the lumped element hypothesis is satisfied [for abs k ̃ d < 0.5] and the radiation impedance is negligible (for k R < 0.5, where k is the wavenumber in air and R is the radius of the tube in which the measurements are carried out). It is shown that, by means of the measurements in two configurations with (full) and without (empty) the tested material, the accurate evaluation of the radiation impedance at the open-end section are not required.

In this work, an acoustic lumped element technique has been developed to measure the dynamic bulk modulus of porous materials in the low frequency range ( f<500 Hz). Based on the electroacoustic analogy of wave propagation inside a porous medium, an analytical derivation of the measurement method is given. Unlike other techniques, it requires the use of only two microphones placed in the cavity containing the sample being tested and in the loudspeaker box. The proposed method provides reliable results when the longitudinal viscous impedance within the medium is negligible with respect to the transversal thermal impedance. The upper limit of the frequency validity range can be determined from the relationship absk̃d≈0.5, where k̃ is the acoustic wavenumber of the porous material and d is the sample thickness. Furthermore, some practical aspects related to the measure are also reported. To validate the methodology, experimental campaigns have been performed on different typologies of materials (fibrous, uniform cross-section geometries, additive manufactured sample, and foam) in two laboratories. The experimental results show good agreement with the theoretical results within the frequency validity range.

Many noise control applications are based on the use of porous materials; therefore, it is important to have a tool to simulate acoustic behaviours. Plane-wave acoustic properties such as the sound absorption or reflection coefficient at normal incidence can be quickly obtained using standing wave tube or theoretical models and can be used to select the type of porous material and its dimensions. However, in real situations, no plane wave exists, and the sound field is more complex. Therefore, it is interesting to understand the real behaviour of porous materials. In this paper, a simple case of a point source above a uniform infinite layer of porous material has been analysed. Conversely, to the case of a plane wave excitation, on the porous material surface different incidence angles can be observed and the phase relation between the pressure and the particles velocity should be considered. The aim of this work is to define the far and the near field above a porous material where the results obtained considering a plane excitation may or may not be respectively extended. For this purpose, two parameters have been introduced: the energetic deviations index and the true reflection angle.

Air-flow resistivity is a main parameter governing the acoustic behavior of porous materials for sound absorption. The international standard ISO 9053 specifies two different methods to measure the air-flow resistivity, namely a steady-state air-flow method and an alternating air-flow method. The latter is realized by the measurement of the sound pressure at 2 Hz in a small rigid volume closed partially by the test sample. This cavity is excited with a known volume-velocity sound source implemented often with a motor-driven piston oscillating with prescribed area and displacement magnitude. Measurements at 2 Hz require special instrumentation and care. The authors suggest an alternating air-flow method based on the ratio of sound pressures measured at frequencies higher than 2 Hz inside two cavities coupled through a conventional loudspeaker. The basic method showed that the imaginary part of the sound pressure ratio is useful for the evaluation of the air-flow resistance. Criteria are discussed about the choice of a frequency range suitable to perform simplified calculations with respect to the basic method. These criteria depend on the sample thickness, its nonacoustic parameters, and the measurement apparatus as well. The proposed measurement method was tested successfully with various types of acoustic materials.