We study the radial breathing mode (RBM) of resonant single walled carbon nanotubes within individual bundles. As strain is applied, significant debundling of the nanotubes occurs, causing an upshift in the RBM frequency. The RBM frequency is found to change irreversibly with strain, correlating more strongly with the total number of strains and relaxations than with absolute strain, indicating that debundling is the dominant cause of the observed changes. The RBM upshift of semiconducting nanotubes is 70% larger than that of metallic nanotubes. We also observe a large drop in the Raman intensity as the nanotubes are debundled. This drop is not due to a change in the resonant electronic transition energies of the nanotube and indicates that neighboring nanotubes within a bundle play an important role in the resonant nanotube's Raman signal.