Existing studies suggest that wavy leading edges (WLEs) offer substantial reduction of broadband noise generated by an aerofoil undergoing upstream vortical disturbances. In this context, there are two universal trends in the frequency spectra of the noise reduction which have been observed and reported to date: (i) no significant reduction at low frequencies followed by (ii) a rapid growth of the noise reduction that persists in the medium-to-high frequency range. These trends are known to be insensitive to the aerofoil type and flow condition used. This paper aims to provide comprehensive understandings as to how these universal trends are formed and what the major drivers are. The current work is based on very-high-resolution numerical simulations of a semi-infinite flat-plate aerofoil impinged by a prescribed divergence-free vortex in an inviscid base flow at zero incidence angle, continued from recent work by the authors (Turner & Kim, J. Fluid Mech., vol. 811, 2017, pp. 582–611). One of the most significant findings in the current work is that the noise source distribution on the aerofoil surface becomes entirely two-dimensional (highly non-uniform in the spanwise direction as well as streamwise) at high frequencies when the WLE is involved. Also, the sources downstream of the LE make crucial contributions to creating the universal trends across all frequencies. These findings contradict the conventional LE-focused one-dimensional source analysis that has widely been accepted for all frequencies. The current study suggests that the universal trends in the noise-reduction spectra can be properly understood by taking the downstream source contributions into account, in terms of both magnitude and phase variations. After including the downstream sources, it is shown in this paper that the first universal trend is due to the conservation of total (surface integrated) source energy at low frequencies. The surface-integrated source magnitude that decreases faster with the WLE correlates very well with the noise-reduction spectrum at medium frequencies. In the meantime, the high-frequency noise reduction is driven almost entirely by destructive phase interference that increases rapidly and consistently with frequency, explaining the second universal trend.