# Porous Materials Essay

2.1 Porous Materials

For the purposes of this report, porous materials is defined as a medium containing voids[2]. The skeletal material is called the matrix and the voids are filled with a fluid (usually air). The physical properties of the materials can be characterised by bulk, macroscopic and microscopic properties. Most of which have an impact on the acoustical performance of the material.

Sound energy is lost in porous materials when it is transformed into heat. This is caused by a combination of effects. Firstly, there are losses through the viscous effects between the solid matrix and the fluid when pressure waves causes the fluid to move longitudinally [3]. Secondly, pressure waves causes the skeletal structure

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This is analogous to an electrical system when electrical flow is opposed it causes a voltage applied to the system. In acoustics, the impedance is defined as the ratio of pressure to flow.

2.1.2 Micro Properties

It is at the micro scale at which the material acts with the fluid. Micro properties are the geometry details that define the interaction between sound and the material what define the Macro properties.

Flow resistivity (r) is the ratio of a static pressure drop to the corresponding volume flow (U) rate for a sample length (d). It is a measure of how well fluid can flow through a material and the resistance it encounters. This is an important aspect in acoustic materials as sound waves is essentially movement of fluid in the longitudinal direction.

2.2 Models

Using the microscopic properties of the porous media, it is possible to predict the acoustical performance. The values obtained from using these relationships will be verified using a testing method discussed later on in this report.

2.2.1 Dunn & Davern

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U=A_p/S_s v

Where Ss is the cross sectional area of the sample, and v is the terminal velocity of the mass which is obtained by timing how long the mass takes to travel a defined length.

The flow resistivity is thus: r=(CMgcos(ψ) S_s t)/(LA_p^2 )

A correction factor (C) [9] is used to account for leakage between the mass and the pipe wall, as well as the friction between the two surfaces. The angle at which the pipe is positioned from the vertical is ψ.

2.3.2 Microphone Method of Measuring Flow Resistance

The alternative method of measuring flow resistance is using an impedance tube [10]. The sound source used is a pure tone and is adjusted so the distance between each microphone is exactly an odd number of quarter wavelengths. A frequency of less that 100Hz should be used to minimise the effects of flow reactance. The sample is placed adjacent to the first microphone.

The flow resistance using this method is given by: r=(ρ_0 c)/l 〖10〗^((L_p1-L_p2)/20)

Where L¬¬p1 and Lp2 are the pressures measured from each microphone