Scattering of surface water waves involving a vertical barrier with a gap

A mixed boundary-value problem associated with scattering of surface water waves by a vertical barrier with a gap of an arbitrary length is solved completely by the aid of the solution of a special logarithmic singular integral equation in the domain (a, b), which has bounded behaviour at both the end points a(> 0) and b. The reflection coefficient is obtained analytically and its numerical values are presented graphically, for different values of the ratio of the width of the gap to the position of the gap. The present method of solution replaces the existing methods, which are either more elaborate or approximate in nature.