Energy and momentum transport in string waves

Abstract

Formulas are derived for the energy, momentum, and angular momentum transmitted by waves of arbitrary shape in an inextensible string and by pure transverse waves in a suitably extensible string. The analysis is based on Tait’s procedure of viewing the wave from a moving frame of reference, and its application to the inextensible string, at least, is simple enough for use in elementary physics courses. The same method is used to find the elastic condition on an extensible string necessary for the propagation of mutually coherent shape and density waves. It is shown that the perfect transverse string waves referred to in textbooks can only be propagated in strings of the ideal Slinky spring type, and that they are incapable of carrying net momentum.