jats:pThe scattering of sound by a finite rigid plate with a finite poroelastic extension interacting with an unsteady acoustic source is investigated to determine the effects of porosity, elasticity and the length of the extension when compared to a purely rigid plate. The problem is solved using the Wiener–Hopf technique, and an approximate Wiener–Hopf factorisation process is implemented to yield reliable far-field results quickly. Importantly, finite chord-length effects are taken into account, principally the interaction of a rigid leading-edge acoustic field with a poroelastic trailing-edge acoustic field. The model presented discusses how the poroelastic trailing-edge property of owls’ wings could inspire quieter aeroacoustic designs in bladed systems such as wind turbines, and provides a framework for analysing the potential noise reduction of these designs.</jats:p>