Waveguides with two soft and two hard boundaries, operated near the cut-off frequency. (a) Calculated transmission phase and amplitude. The design parameters are similar to the experimental setup, with only the length being modified (a = 0.225 m, b = 0.382 m, and d = 12.6 mm). (b) Phase distribution through the CNZ channel near the first cut-off frequency for different lengths. ftunneling (i) = 763.0 Hz, ftunneling (ii) = 763.3 Hz, and ftunneling (iii) = 764.9 Hz. (c) Spatial variation of phase at the CNZ tunneling frequency for waveguides with 90° and 180° bends. We observe uniform phase despite bending of the channel. Here, ftunneling_90 (i) = 755.10 Hz, and ftunneling_180 (ii) = 756.52 Hz.