Reply to comments on 'Energy in one-dimensional linear waves in a string'

In this reply we respond to comments made by Repetto et al and by Butokov on our letter (Burko 2010 Eur. J. Phys. 31 L71-7), in which we discussed two different results for the elastic potential energy of a string element. One derived from the restoring force on a stretched string element and the other from the work done to bring the string to a certain distorted configuration. We argue that one cannot prefer from fundamental principles the former over the latter (or vice versa), and therefore one may apply either expression to situations in which their use contributes to insight. The two expressions are different by a boundary term which has a clear physical interpretation. For the case of standing waves, we argue that the latter approach has conceptual clarity that may contribute to physical understanding.