Time domain modelling of sound attenuation by porous materials

Porous materials are renowned for their ability to attenuate sound. As sound wave penetrates the pores, the air oscillates and friction occurs due to its motion relative to the pore walls. Friction and heating always come together - ancient people even produced light by rubbing stones! A lot of sound energy is transferred into heat in pores which leads to its attenuation.In many materials size and shape of the pores vary unpredictably across the sample. For this reason it is difficult to know exactly what happens within them. Luckily, some macroscopic material parameters can give indirect information about its pores. For instance by weighing the sample one can find the porosity, which indicates the volume fraction occupied by pores. Once all such parameters are known, the mathematical formula can be constructed out of them, which predicts effectiveness of attenuation of a certain frequency sound by the porous material. The exact formula however is only known for very high and very low frequency sound, what combination of parameters has to be used for the rest of the frequencies is not known exactly. For these frequencies the model for sound attenuation is constructed empirically, i.e. the formula is devised which gives correct results for low and high frequencies and at the same time provides good fit with the majority of data for the intermediate frequencies.Quite often the sound signal to be attenuated is not continuous but pulsed. Sound from explosions for instance only lasts for several milliseconds. However even in this case the signal can be thought of as an infinite sum of continuous sounds with all possible frequencies. In principle, if the signal is not very loud, it is possible to consider the attenuation of every frequency component by porous material and then sum the results and see what happens with the whole pulse. In reality, this procedure requires a lot of computer time. Moreover, if the pulse amplitude is high, its frequency components interact with each other as it propagates and hence can't be considered separately. That is why the project focuses on the time - domain model of pulse attenuation: it does not use expansion into frequency components but looks at the pulse as a whole. Its aim is to develop an empirical time domain model, similar to those existing for continuous sounds of specific frequency, working for any duration pulse, loud or not. When designed, such a model will most definitely result in equations which are too difficult to be handled without the use of computers. In fact, it is anticipated that the considerable part of the project will be devoted to finding fast and effective ways to solve them numerically. We will start from a simpler version of the model assuming that sound only propagates in pores, but not through the solid matrix of the material. To validate the model, the laboratory transmission measurements on heavy materials with simple pore geometry will be carried out.The ultimate goal of the project, however, is to develop a model working well for naturally occurred porous materials (like soils, sands and gravel), which can be used to attenuate sound outdoors. When sound hits some of these materials not only air in pores oscillates, but the solid granules themselves can be involved in motion. This situation requires further refinement of the model and further measurements on natural porous materials.The project will have two major outcomes:1. The model and the numerical algorithm can be used by scientists dealing with any aspects of pulsed sound interaction with porous materials, most likely in atmospheric and room acoustics.2. We will provide practioners involved in noise control, with a guide about what kind of porous material should be used for attenuation of sound pulses in each particular practical situation. The choice will depend on how long and loud the pulse is, what shape it has and what are the requirements for its attenuation.