# Noise Control in Air Mechanical Ventilation Systems with Three-Dimensional Metamaterials
## 3 Materials and Methodologies  
Since it was not possible to perform field measurements on real plants, the authors developed a measurement system in a laboratory. A sound source (RCF TWT 50) has been powered with a sine sweep signal generated by the Clio board simulating the fan noise of the mechanical system. The sound source was placed at one end of a tube having dimensions equal to 40 \(\times\) 30 \(\times\) 50 cm, standing on a layer of a sound absorbing material in order to lower unwanted reflections. On the opposite side of the tube, a condenser microphone was placed (Audiomatica 1/4-inch). An audio system (Clio hardware and software) was used to control the emission and the recording of the sound signal [30]. The Clio is a time-invariant system provided with only one channel. Impulse responses (IRs) were analyzed in the frequency range of 1 kHz and 10 kHz for both configurations, with and without filter under test. The insertion loss (IL) and the sound attenuation were calculated as the difference between the levels measured without filter (LFF) and with the filter in place (Lfilter), as shown in Equation (2). \[f_{BG}=\frac{c}{2\alpha\ \sin(\Phi)} \tag{2}\]  
During the acquisition, the number of samples processed by each FFT was equal to 65,000, while the frequency sample rate was 48 kHz. The acoustic measurements were performed with the extremity of the tube open (free field). The tested spheres had a diameter of 24 mm, made of solid polystyrene. The choice of this lightweight material for the acoustic tests would be closer to the future realization of the spheres intended to be made with recycling materials, such as solid plastic or resins with wooden chipboard particles. The spheres were piled for the same filter and were staggered of half-sphere diameter with respect to the successive layers in order to interrupt the direct sight between source and receiver. Figure 3 shows the schematic configuration and the real filters realized for the acoustic measurements [31; 32; 33; 34]. Note that the distance between the loudspeaker and the closest layer of spheres was constant and equal to 400 mm; the same distance has been kept constant between the microphone and the last layer of spheres. Figure 3: Configuration system used for the acoustic measurements: scheme out of scale (**a**), real filters (**b**). The goal of testing different configurations of filters consists of collecting robust data output in order to compare the sound attenuation attributed to the spherical scatterers. A summary of the adopted configurations is described as follows:  
* **Configuration 1**: the metamaterial filter is composed of one layer of spheres. * **Configuration 2**: the metamaterial filter is composed of two layers of spheres with a gap distance in between equal to 10 mm. * **Configuration 3**: the metamaterial filter is composed of two layers of spheres with a gap distance in between equal to 20 mm. * **Configuration 4**: the metamaterial filter is composed of two layers of spheres with a gap distance in between equal to 30 mm. * **Configuration 5**: the metamaterial filter is composed of two layers of spheres with a gap distance in between equal to 40 mm. * **Configuration 6**: the metamaterial filter is composed of three layers of spheres with a gap distance equal to 10 mm between the first and the second layer, and with a gap distance equal to 20 mm between the second and the third layer. * **Configuration 7**: the metamaterial filter is composed of three layers of spheres with a gap distance equal to 20 mm between the first and the second layer, and with a gap distance equal to 20 mm between the second and the third layer. All the described configurations are summarized in Figure 4, where the blue cone stands for the loudspeaker, the green square represents the microphone, and the red spheres represents the acoustic filter. Table 1 summarizes the parameters that characterize each configuration.