Normalized RMS pressure vs. position relative to the end of the pipe for a square pipe at 875 Hz. Top: standing-wave (inside) fit; bottom: radiating-wave (outside) fit. The gray shading indicates points excluded from the fit and was determined using equation (2). The LS fit (solid blue line) shows better phase alignment near δ inside compared to the empirical fit (dashed orange line), consistent with the lower SSE in Table 2; outside, the 1/(x + δ) decay is essentially identical for both models.