The overarching goal of this analysis, and many like it, is to develop our understanding of the strong force interactions within the nucleon by examining the nature of their excitation spectra. As the resonances of these spectra have very short lifetimes (τ = 1 × 10 −23 s) and often have very similar masses, it is often impossible to directly observe resonances in the excitation spectra of nucleons. Polarization observables allow us to study the resonances by looking at how they affect the spin state of final state particles. The beam asymmetry is a polarization observable that allows us to detect the sensitivity of these resonances, and other transition mechanisms, to the electric vector orientation of incident photons. Presented in this thesis are first measurements of the beam asymmetries in the resonant region for the reaction channel γp → pπ + π − focusing on the intermediate mesonic states ρ 0 and f 0 , and the final state pions. The analysis used data from the g8b experiment undertaken at the Thomas Jeffereson National Accelerator Facility(JLab), the first experiment at JLab to use a linearly polarized photon beam. Using the coherent Bremsstrahlung facility and the CLAS detector of Hall B at JLab allowed for many multi-channel reactions to be detected and the first measurements of many polarization observables including those presented here. A brief overview of the theoretical framework used to undertake this analysis is given, followed by a description of the experimental details of the facilities used, then a description of the calibration of the Bremsstrahlung tagging facility which the author undertook, and finally the analysis is presented and the resulting measurements. i Declaration I declare that I composed this thesis in its entirety and that the work presented was completed by myself, except in the cases where the works of others have been explicitly referenced.