To increase wave speed on a string, one must consider both tension and mass per unit length. The wave velocity is determined by the formula v = (T0/ρ)½, where T0 is the tension and ρ is the mass per unit length. Decreasing the string thickness increases wave speed if tension remains constant, as it reduces the mass per unit length. Therefore, string thickness does impact wave velocity. Understanding these relationships is crucial for manipulating wave speed effectively.