Power spectrum of the spherically averaged radial velocity for model C. The grey curve shows the averaged power spectrum (normalised so that its maximum is unity) of the spherically averaged radial velocity, computed over the radial range 80−100% of R_*. The black curve shows the same signal after applying the two-step smoothing procedure (Savitzky-Golay followed by Gaussian filtering), demonstrating the effectiveness of the method in reducing noise while preserving peak structure. Vertical dotted and dashed lines indicate the derived f_mean values and their corresponding bounds f_mean ± f_RMS for the fundamental, first overtone, and second overtone modes, shown in blue, red, and orange, respectively. See main text for further details.