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The boundary element solution procedure for exterior periodic acoustic problems fails at frequencies associated with the eigenfrequencies of the corresponding interior problems. A new technique is developed to overcome this problem in the indirect boundary element method by expanding the integral equations through the application of multi-valued impedance boundary conditions. The effectiveness of this newly developed UNequal Impedance technique for Qualitative Evaluation of acoustic response (UNIQUE) is demonstrated by applying this procedure for the solution a series of exterior acoustic problems.