A metamaterial composed of a set of periodic rigid resonant inclusions embedded in a porous lining is investigated to enhance the sound attenuation in an acoustic duct at low frequencies. A transmission loss peak is observed on the measurements and corresponds to the crossing of the lower two Bloch modes of an infinite periodic material. Numerical parametric studies show that the optimum modal attenuation can be achieved at the exceptional point in the parameter plane of inclusion position and frequency, where the two lower modes merge.