Most cochlea models consider the system as a pair of channels separated by a flexible membrane (basilar membrane). In the part of the wave where the stiffness of the membrane dominates, traveling waves are set up. Because of varying propagation conditions the speed of propagation diminishes most rapidly when the wave approaches the region where the basilar membrane shows resonance for the frequency under consideration. It might be expected that such a rapid change of propagation velocity gives rise to reflection. In this paper a one-dimensional model is considered in such a way that resonance properties stand out clearly. The results show that even when extremely little damping occurs (damping factor less than 10(-3)) virtually no reflection is evident. under conditions of low damping the nature of the response is such that it is incompatible with inner hair cell or nerve fiber responses from the cochlea: some kind of "sharpening mechanism" should be present. Limitations of the model considered should be studied further to verify the conclusions in more general cases. Despite these limitations the present model serves to illustrate typical physical phenomena, like reflection and energy dissipation, quite well.