Fig. 1. (A) Two-dimensional strip oscillating with amplitude h₀ and moving forward at velocity U while a wave passes rearward at velocity c. The amplitude changes from the leading to the trailing edge by a factor , the ratio of h to h₀. The instantaneous location of a point (x) on the strip is described by h(x,t), where t is time. (B) A ratfish with a wave (highlighted) traveling backwards on its pectoral fin at wave speed c. (C) Diagram of a ratfish illustrating the angle () subtended by a flapping fin and tip amplitude (H).