# An Experimental Study of the Performance of a Crossed Rib Diffuser in Room Acoustic Control
## 2 Specification and Acoustic Properties of CRD
### Scattering Characteristics  
We evaluated the random-incidence scattering coefficients of the fabricated CRD and compared the obtained results with those for R-1, R-2, a two-stacked R-1 (R-1-W) and a two-stacked R-2 (R-2-W). As the CRD was a diffuser having a two-dimensional structure, the scattering coefficient was measured using a 1/5 scaled reverberation room, in which the 1/5 scaled test specimen was placed on wooden circular base. The use of a scale model for the scattering coefficient is recommended in [9]. Measurements for random-incidence scattering coefficients were conducted in accordance with ISO 17497-1 [5] and Sakuma and Lee [19]. The reverberation room's volume and the circular base diameter were 212 m\({}^{3}\) and 3.75 m, respectively, at 1/1 scale. In fact, the 1/5 specimen of CRD was constructed using square members with 5 mm edge length. Additionally, the respective period lengths of R-1 and R-2 were 1 and 20 mm because of the availability of square members. The 1/5 model of the crossed rib diffuser located in the 1/5 reverberation room is shown in Figure 3. For impulse response measurements in the 1/5 reverberation room, two source points and three receiver points were set up. A swept-sine signal with signal length of 1.365 s was used as a sound source signal. A rotation period was set to 162 s/rev. To measure the reverberation time in the rotating condition, we used the continuous method wherein 119 signals were emitted during the circular table rotations. To reduce the edge diffraction effects, the edge of the circular base was covered with a 1-mm-thick plastic plate.  
The random-incidence scattering coefficients of 1D periodic rib diffusers were calculated using _AMFG Reflex_[20], where the correlation scattering coefficient proposed by [PERSON] [4] was evaluated using the two-dimensional boundary element method. To reduce the effect of edge diffraction, each 1D periodic rib diffuser was modeled with 11 periods. Though the theoretical background of the correlation scattering coefficient is different from that of the reverberation room method, with random-incidence, the correlation scattering coefficient is theoretically nearly equivalent to the measured scattering coefficient in the reverberation room [21].  
Figure 1: Cross-sections of R-1 (**Upper**) and R-2 (**Lower**).  
Figure 2: Manufactured samples: R-1 (**Left**); R-2 (**Center**); and crossed rib diffuser (**Right**).  
Figure 4 presents a comparison of random-incidence scattering coefficients of various rib-type diffusers. R-1 and R-1-W, respectively, showed peaks at 2.5 kHz and 3.15 kHz. However, they also present large declines before and after the peaks, leading to a narrow frequency band with high scattering coefficient, which is a typical shortcoming of 1D periodic rib diffusers. R-2 shows the low scattering coefficient in broadband. R-2-W presents the peak of scattering coefficient at 1.25 kHz, but the peak value is smaller than 0.4. The CRD shows an increase in the scattering coefficient with frequency. Additionally, the CRD scattering coefficient has a peak at 2.5 kHz and a dip at 3.15 kHz, derived from the structural property of R-1, the lower part of CRD. However, the declines in the scattering coefficient before and after the peak were reduced more than those of R-1 and R-1-W. This result demonstrates that the two-stage crossed structure of CRD overcomes the shortcoming of 1D periodic rib diffusers, engendering a higher scattering coefficient in a wide band.