3.1.1. Time Domain Analysis

The results for the T-junction and shown in Figure 3. Ports are denoted as in Figure 1, and it is apparent that when the junction is excited at port 1 the pulse transmitted through port 2 (i.e., in the main propagation direction) has a higher amplitude than that transmitted through port 3 (the branched duct), as could be intuitively expected. It is also apparent, and equally expectable, that when the junction is excited at port 3, the pulses transmitted through ports 1 and 2 are very similar, the small differences observed being attributable to manufacturing issues.

Differences in the reflected pulses recorded at ports 1 and 3 are also apparent, even if the incident pulses do not have the same amplitude. The reflected pulse recorded at port 3 is noisier, and its

amplitude is comparable to that of the reflected pulse recorded at port 1, while the corresponding incident pulse has a lower amplitude. This indicates that reflection is more intense when the junction is excited at the branch duct, as it is also intuitively reasonable in terms of the interaction of the incident pulse with the wall of the main duct. Of course, none of these effects, regarding both transmission and reflection, can be accounted for by a constant pressure model, and this is the reason why such a model will not be considered in the subsequent discussion.

**Figure 3.** Experimental results for the T-junction in the time domain. (**a**) Excitation at port 1; (**b**) excitation at port 3. Ports are denoted as in Figure 1.

The results for the Y-junction are shown in Figure 4. Here the trends observed confirm those found for the T-junction regarding the difference between the main duct and the branch duct, but with additional issues related with the branch angle. Comparison of Figure 4a,b indicates that the difference in amplitude between the two pulses transmitted is more important when the branch direction is against that of the incident pulse (i.e., when the junction is excited at port 2), in which case the results are rather similar to those shown in Figure 3a for the T-junction. Regarding the reflected pulses recorded at ports 1 and 2, some differences may be observed mostly in the last part of the pulse, which suggests some difference in the dynamic behavior of the junction.

**Figure 4.** Experimental results for the Y-junction in the time domain. (**a**) Excitation at port 1; (**b**) excitation at port 2; (**c**) excitation at port 3. Ports are denoted as in Figure 1.

These statements are supported by the results obtained with the excitation at port 3, shown in Figure 4c. Here, it appears that again the amplitude of the transmitted pulse is higher when there is no significant change in direction along the transmission path (in this case, from port 3 to port 1). However, the differences are not as apparent as those seen in Figure 4b, which is reasonable considering that here there is some change in direction in the two transmission paths. It is also worth noticing the clear differences observed between the reflected pulse recorded at port 3 and those recorded at the other two ports. A much more complex time evolution can be observed in the case of port 3, which again suggests that wave dynamics inside the junction depend significantly on the port at which the junction is excited.
