How does the amplitude of a wiggle on a string change when the string is stretched? We answer this question for both longitudinal and transverse wiggles and for arbitrary equation of state, {\it i.e.}, for arbitrary relation between the tension $τ$ and the energy per unit length $ε$ 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.

Written with ReVTeX 3.0 package. Two figures are not included. Complete paper with postscript figures can be retrieved through anonymous ftp @quark.phys.ufl.edu. Get /preprints/ifthep94_4.tar.gz, gunzip and tar it. UFIFT-HEP-94-4