Stretching wiggly strings.

How does the amplitude of a wiggle on a string change when the string is stretched We answer this question for both longitudinal and tranverse wiggles and for an arbitrary equation of state, i.e., for an arbitrary relation between the tension [tau] and the energy per unit length [epsilon] of the string. This completes our derivation of the renormalization of string parameters which results from averaging out small scale wiggles on a string. The program is presented here in its entirety.