**Appendix A. Experimental Procedure**

Making reference to the notation in Figure 2, the determination of the transmission and reflection coefficients defined in Equation (1) requires the three following measurements:

*Appl. Sci.* **2017**, *7*, 480

• Excitation in duct 1, with anechoic terminations in ducts 2 and 3, so that *A*1 = 0 and *A*2 = *A*3 = 0, and thus,

$$R\_1 = B\_1 / A\_1; \; T\_{12} = B\_2 / A\_1; \; T\_{13} = B\_3 / A\_1 \,. \tag{A1}$$

• Excitation in duct 2, with anechoic terminations in ducts 1 and 3, so that *A*2 = 0 and *A*1 = *A*3 = 0; then,

$$R\_2 = B\_2 / A\_2; \ T\_{21} = B\_1 / A\_2; \ T\_{23} = B\_3 / A\_2 \,. \tag{A2}$$

• Excitation in duct 3, with anechoic terminations in ducts 1 and 2, so that *A*3 = 0 and *A*1 = *A*2 = 0, so that,

$$R\_3 = B\_3 / A\_1; \; T\_{31} = B\_1 / A\_3; \; T\_{32} = B\_2 / A\_3 \, . \tag{A3}$$

In order to perform the above-indicated tests, the modified version of the impulse method described in [28] was used, since pressure components, which all the previous developments are based upon, are directly obtained in the time domain with a simple procedure, and the consideration of three-port elements is straightforward. In Figure A1 both the experimental setup used and the relevant pressure waves recorded are illustrated.

**Figure A1.** Experimental setup used.

The incident pulse is generated by means of a high speed electrovalve that controls the discharge from a high-pressure tank. A proper choice of the opening time ensures that the spectrum associated with the incident pulse is essentially flat. The length of the ducts placed between the valve and transducer 0, transducer 0 and the junction, and the junction and the open ends is chosen so that no windowing is necessary in order to isolate the incident, the reflected, and the transmitted pulses, as indicated in the figure. Transducer 0 was located 15 m away from both the valve and the junction, and transducers 2 and 3 were placed 0.15 m downstream of the junction, and 15 m away from their corresponding open end.

At the position indicated for transducer 1 in Figure 2, it is clear that this transducer records the addition of the incident and the reflected pulses, as illustrated in the figure. In order to surpass this difficulty, the solution adopted is to estimate the pulse incident on the junction at section 1 (whose Fourier transform will give the complex amplitude of the *A*1 component) from an additional test performed without any element, using the pressure recorded by transducer 0 only to check the comparability of the excitations used in both types of tests (with and without junction).
