With a background in fluid mechanics perhaps my perspective on the traveling wave helps the discussion.
I don't think there is a question whether or not there is a traveling wave in the cochlea. Fluid mechanics dictates that there has to be one.
The confusion comes - I think - from comparing the basilar memebrane with a string where the energy is passed on through the string and it is that same string which is showing the movement. In this respect the comparison with surface waves on water is much appropriate. The fluid-air interface is showing the movement, but it is the underlying fluid which passes
on the motion. Imagine a pond surface covered with ducks. Imagine it to be covered so densely you cannot see the water surface. When the water is set in motion (not neccessarily at its
surface), the ducks will move. This motion will look like a wave and I guess everyone would agree with the use of the term travelling wave in this case. The energy causing the
ducks to move is not passed on from one duck to the other, but stems from the motion of
Likewise in the cochlea the BM motion is caused by motion of the fluid. The fact that we
have fluid on both sides of the BM, whereas in the example we have fluid below and air on
top can be shown (mathematically) to be of no consequence for the principle. Also the
fact that in the example the restoring force acting on the ducks is gravity, whereas in
the cochlea it is the BM stiffness does not affect this story.
The main problem with the resonator/resonance theory (at least in the versions I know) is
that the motion of neighbouring resonators is independent. In the example neighouring ducks can not move independently because their motion is linked through the motion of the underlying (continous) water.
Complicating factor in the discussion is perhaps that in the cochlea, the restoring force being stiffness combined inevitably with mass, we automatically get resonators. So in my view it
is not a question of resonance OR travelling wave. It has to be a bit of both.
Fluid mechanics dictates that there is a travelling wave on the basilar membrane unless cochlear fluid is unlike any other fluid I know. The question that may remain is whether this wave motion is what causes the effective stimulation of haircells. But there should not be a question whether or not there is a traveling wave, even if it has not been shown
definitively in measurements.
The problem I see with a compression wave being the stimulus and the haircells acting as pressure sensors is that. This assumes that the haircells will be compressed by a pressure acting on them form the outside. However, the haircells are filled with fluid themselves and there will be no pressure difference between the inside and outside of the cell. This implies that the cell wil not deform and I do not quite see how the sensor would then operate. (But the fact that I don't see it does not mean it impossible, of course...).
The references to texts already given by dr Frosch and others are excellent and I don't have much else to add.
All the best,
Peter van Hengel