## 4 Primary and Secondary Paths
### Secondary Paths Analysis  
The secondary path is a path between the input signal to one of the actuators (exciters) mounted on the inner side of the active casing panels, and the signal acquired by one of the error microphones. Selected secondary paths amplitude responses are presented. In Figure 7, secondary paths between the selected five actuators (one per casing panel), and the error microphone corresponding to right casing panel are presented. The casing was placed at  
Figure 5: The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the top casing panel. Figure 6: The amplitude functions of the frequency functions of the impulse response estimates for the paths between one of the room microphones and the primary source for the eight different distances between the active casing and the wall. a distance \(d_{1}=0.1\) m. It is the smallest considered distance of \(d_{i}\), where there are significant differences in paths' magnitudes, depending on chosen setup (right error microphone placed at location R or R\({}^{\prime}\)). In Setup 1 (location R), magnitudes are much greater than in Setup 2 (location R\({}^{\prime}\)). As it could be expected, the actuator mounted to the right panel contributes the most to the signal obtained with the right error microphone when placed at location R. However, other secondary paths are also stronger when the error microphone is placed at location R (Setup 1) compared to location R\({}^{\prime}\) (Setup 2). This means that the narrow gap between the casing panel and the corner wall causes a resonance, amplifying sound generated by any actuator, mounted to any of the casing panels. In Figure 8, secondary paths between the selected actuator mounted to the right panel and the right error microphone are presented for all distances \(d_{i}\). Magnitudes are in general greater in Setup 1 (Figure 8a), especially when \(d_{4}\leq 0.4\) m. In nearly the whole considered frequency range, magnitude increases as the distance \(d_{i}\) decreases. In Setup 2 (Figure 8b) such effect is not visible. Similar observations can be drawn from Figure 9, which presents responses of secondary paths between back casing panel's selected actuator and the back error microphone at all distances. In Setup 1 magnitude increases as the distance \(d_{i}\) decreases. On the other hand, in Setup 2 such effect is also visible, but only in a frequency range up to about 200 Hz. This shows that the narrow gap amplifies most of the considered frequencies if a microphone is placed in the gap (location B). However, the actual emission (sound field excitation in the laboratory enclosure) can be slightly enhanced, due to casing placement in the corner, only in a limited range of low frequencies (as the measurement at location B\({}^{\prime}\) shows). Figure 8: The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between right casing panel’s selected actuator and the error microphone adjacent to the right casing panel, at all distances, in both setups. Figure 7: The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between each casing panel’s selected actuator and the error microphone adjacent to the right casing panel, at a distance of 0.1 m, in both setups. In Figure 10, secondary paths between top casing panel's selected actuator and the top error microphone are presented at all distances. Amplitude responses for both setups (Figure 10a,b) are similar, confirming the consistency of obtained results. Similarly as for the back microphone placed at location B\({}^{\prime}\), slight enhancement of magnitude for low frequency range up to approximately 180 Hz can be observed when the distance \(d_{i}\) decreases. In Figures 11 and 12, the paths between selected actuators and one of the room microphones are presented. The room microphones are in constant locations during all experiments.