In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the considered wave pulse and the related velocity and acceleration distributions. In this paper, we derive the named formula by applying Newton's second law or the work-energy theorem to a finite element of the string, making no assumptions about the shape of the wave. We argue that the suggested method can help the student gain a deeper insight into the nature of waves and the related process of energy transport, as well as provide a new experience with the fundamental principles of mechanics as applied to extended and deformable bodies.