VRIJE UNIVERSITEIT BRUSSEL Acoustics - the Dept. of ...

64 CHAPTER 4. SOUND ABSORPTIONabsorbing materials is close to that of air. Seen that this impedance is rathersmall (∼ 400 rayl), it is not easy to find solid materials which absorb enoughsound. However, there exist alternative solutions for the physical realizationof sound absorption, based on other phenomena :A plate on a layer of airHelmholtz resonatorPorous acoustic absorbing materialsFollowing sections will give an overview of these three methods.4.2 Realization of acoustic absorption4.2.1 Plate on an air layerA plate on an air layer belongs to the category of resonant absorption means.Onefixes aplate (plywood, chipboard, sheet metal, hardboard, plasterboard,etc.), using wooden slats or profile irons, at a distance of some centimetersin front of a hard wall (see Figure 4.4). The plate, together with the airbehind it, constitutes a mass-spring system. The plate represents the mass,while the air represents the spring element. In fact the plate has also someresilience, but it can be shown that its influence is negligible once the plate isof a certain size (starting from 1 m x 1m). The method of attachment of theplate is therefore almost of no importance, i.e. one may reason on a highlysimple physical model: a plate freely suspended on an air cushion of a fewcm thickness. The wave length of sound is supposed to be much bigger thanthe thickness of the air cushion, so no wave phenomena occur. Let :m mass per square meter of panel surface,d damping per m 2 ,k the stiffness coefficient of the air layer behind the plate,p the excitation force per m 2 , i.e. the sound pressure incident on the plate.then one can find for this model with one degree of freedom :mẍ+dẋ+kx = p (4.11)or by writing the equation in function of the particle velocity v :∫m˙v +dv +k vdt = p (4.12)