This animation shows a simulation of "travelling wave motion" in the basilar membrane in response to a sound composed of two frequencies (1000 and 2500 Hz). The sound waveform is shown in the top panel, the basilar membrane response is shown below. Since the frequency components of the input are separated by more than an octave, they are well separated by the mechanical filtering of the cochlea, producing clearly separated "travelling waves" for each frequency component.
Note that this simulation is based on a simple, linear gamma-tone filter model of the cochlea, as described in chapter 2 of "Auditory Neuroscience". (It was created using Matlab, together with the GammaTone Tool Kit). The amplitude of the basilar membrane motion is massively exaggerated. Also, real basilar membrane motion is quite a bit more complex due to the nonlinearities introduced by the motion of outer hair cells, which make the basilar membrane much more sensitive to very weak sounds and help our auditory system cope with an enormous range of possible sound amplitudes, but which can also lead to significant distortions.