  This paper presents an analytic solution for the sound generated by an
unsteady gust interacting with a semi-infinite flat plate with a serrated
leading edge in a background steady uniform flow. Viscous and non-linear
effects are neglected. The Wiener-Hopf method is used in conjunction with a
non-orthogonal coordinate transformation and separation of variables to permit
analytical progress. The solution is obtained in terms of a modal expansion in
the spanwise coordinate, however for low- and mid-range incident frequencies
only the zeroth order mode is seen to contribute to the far-field acoustics,
therefore the far-field noise can be quickly evaluated. The solution gives
insight into the potential mechanisms behind the reduction of noise for plates
with serrated leading edges compared to those with straight edges, and predicts
a logarithmic dependence between the tip-to-root serration height and the
decrease of far-field noise. The two mechanisms behind the noise reduction are
proposed to be an increased destructive interference in the far field, and a
redistribution of acoustic energy from low cuton modes to higher cutoff modes
as the tip-to-root serration height is increased. The analytic results show
good agreement in comparison with experimental measurements. The results are
then compared against numerical predictions for the sound generated by a
spanwise invariant line vortex interacting with a flat plate with serrated
leading edge. Good agreement is also seen between the analytical and numerical
results as frequency and tip-to-root ratio are varied.
