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This paper reports on numerical and experimental results of acoustic transmission spectra of bead chains with symmetric and asymmetric Fibonacci-like structures. As a matter of comparison, perfect periodic acoustic waveguide structures are also examined. This study shows that Fibonacci structures with mirror symmetry can exhibit localized modes with higher amplitude, due to resonant transmission induced by the presence of dimers inside the 1D structure. A good agreement is observed between the theoretical predictions and the experimental power spectra.