Diffraction by a rigid barrier with a soft or perfectly absorbent end face

The reduction of noise levels in the shadow region of a rigid barrier of finite thickness is considered when the end face of the barrier is lined with either a soft or a perfectly absorbent material. Solutions, obtained by the method of matched asymptotic expansions, are given for both a semi-infinite barrier and for a finite length barrier placed on a rigid plane. Comparisons are made with existing solutions for barriers that have a rigid end face.