## 3 Experimental Analysis of the Acoustic Cloak
### Experiment Results: Scattering Field Measurement and Visibility Values  
We experimentally investigate the cloak effect in the far field region as a numerical simulation in Section 2.3. The experiment design is consistent with our numerical simulation setup based on the scaling factor \(\sigma=0.38\) of the experiment model defined previously. The sound pressure was measured in the region between \(Ex\) = 0-760 mm and \(Ey\) = 0-190 mm (d\(Ex\) = d\(Ey\) = 19 mm), as shown in Figure 27. The measurement locations of the microphone in the vertical axis are at half the height of the cloak shell. The numbers of field measurement points are 40 points in the \(Ex\) direction with 11 lines in the \(Ey\) direction. The cloak shell and scattering object were placed on a support unit for the experimental measurements. Measurements were performed for three cases: the incident free field (only specimen supporter in the space), the uncloaked object, and the cloaked object. Figure 28 plots the measured sound field results obtained from the RMS values of the sound pressure. As Figure 28a presents the results associated with the free field. In this case, the sound field presented patterns that were clearly flat field value in the result. Some small disturbances were caused by the support unit used in the experiment. Figure 28b,c presents the results of the uncloaked object and cloaked object cases. These results demonstrated similar sound field patterns, which can be attributed to the real experiment environment limit. Some factors in the real experiment, such as the necessary specimen supporter, the directivity difference of the sound source, and the limited physical dimensions in the vertical direction of real test specimen, will produce errors in the measurement results. In order to reduce the influence of these errors, the sound field of Figure 28a was taken as the reference field in order to normalize the other cases. The normalized sound field presented in Figure 29 were obtained by dividing the free field value for obtaining the real effect of the uncloaked object and cloaked object cases. Thereafter, the results are divided by the reference field (free field in Figure 28a) values to reduce the direction uniformity of the sound source and the unnecessary errors in the experiment. Figure 29a,b plot the normalized field results of the uncloaked and cloaked objects, respectively. The field values over 11 wave-front section lines along the \(Ey\) direction in Figure 27 were averaged, and used the Equation (5), then obtained the average visibility value of the cloaked object case \(r_{\text{cloak}}=0.32\). The average visibility value of the uncloaked object case was \(r_{\text{object}}=1.01\), representing an average visibility ratio of \(r_{\text{cloak}}/r_{\text{object}}=0.31\). The value of the cloaked object was 31% that of the uncloaked object and approximately the value of 20% in the numerical simulation. The finding shows the good cloaking effects and it experimentally verified the effectiveness of the proposed cloak shell design. From the research, the cloak effect of the present study is not available in all frequency ranges. The combination of cloak shell layers with different designs, such as the non-scattering coating layer [36]  
Figure 26: Normalized sound field measurements obtained within zone affected by cloak shell: **(a)** the object only; **(b)** the cloak shell only; **(c)** object and cloak shell combined. The red dotted line indicates the space occupied by object.  
in the outer surface layer of the cloak shell, may further improve the cloak performance and provide the cloak of acoustic wave in a wide frequency.  
Figure 28: _Cont._  
Figure 27: The scattering far field was measured using a single free-field microphone scanned in the forward scattering region between \(Ex=0\)–760 mm and \(Ey=0\)–190 mm, as indicated by the dotted line. The measurement step size is 19 mm in both directions.