Re: Answers, comments welcome.

[Willem Christiaan Heerens <heerens1@xxxxxxxxx>]

Dear Randy and List,


Randy, in your message about dichotic stimulation of the basilar membrane 
[BM] you formulated your remarks and asked for answers and/or comments on 
the following topic:

** Do the BM's in a dichotic experiment using two harmonically related tones 
(e.g. 200/300 hz) have the same vibration profile or are they different? **

And you apologized in the following way:
 
** I don't know if this is beyond the scope of this forum in which case I 
apologize. However, if this topic is not too crazy, I would welcome any 
answers, guesses or speculations. **

To my opinion your remarks are to the highest level relevant for everybody 
who is involved in the research of our hearing sense, so also for members of 
this List.
And in my view it is far from crazy.

At the risk of fluttering the dovecote I want to give you my answers and 
comments you asked for.
However for a better understanding of my comments I can only do this in two 
steps.

Please let me first reopen as shortly as possible that other topic issue, 
because it is directly related with the setup of my present answer to you.

In November/December last year we have had the discussion whether a 
traveling wave exists inside the cochlea or on the BM that transfers the 
sound pressure stimulus of a pure tone to the point where, for the 
corresponding frequency, the BM can resonate. Also the model that makes use 
of the transmission line concept was discussed then.

I on my turn presented in that discussion session in a PDF the solution of 
the non-stationary Bernoulli equation, that is perfectly well valid in the 
case of the push-pull movements of the perilymph inside the scala tympani 
[ST] and scala vestibuli [SV], while the in between embedded scala media 
[SM], filled with endolymph at rest, has substantial ? and therefore not 
negligible ? dimensions.
According to hydrodynamic rules these dimensional conditions make that the 
hypothesis in which both the influence of the Reissner membrane and the 
content of the SM can be ignored and the cochlear duct can be considered as 
a folded tube with only the BM as an interface in between is definitely 
invalid.

At the end of that discussion Dick Lion stated that in his opinion the local 
frequency dependent flexibility or compliance of the BM makes it possible 
that this membrane is bending outwards ? a local movement of the BM towards 
the SV ? and that this bending is the cause of evoking sound related stimuli 
in the BM, organ of Corti and finally via the auditory nerve to the auditory 
cortex. 
He therefore firmly disagreed with my point of view and my theoretical work 
couldn?t convince him (and others on this List) that the functional 
mechanism in the cochlear partition might be completely different from what 
is assumed at the moment.

Well like the well-known promoter of physics, MIT professor Walter Lewin, 
does in his magnificent physics courses, I have built my own demonstration 
equipment for clearly showing what happens on the walls of a duct in which 
an alternating flow in core direction is evoked.

The one experimental set-up is extremely simple, but therefore also highly 
convincing.
To mimic utmost compliance in the ?walls? in one of the experiments I have 
hanged on thin wires in an open frame two sheets of paper that can move 
freely. Between the two I can evoke with a spatula an alternating flow 
parallel to the surfaces of the sheets of paper.

And I have constructed a closed loop with a tube and a bellow, the latter 
centrally subdivided by a plate, with which I can create a push-pull flow in 
the tube, while in the other branch of the tube locally a flexible membrane 
is mounted in the wall, which registers what happens on the wall of the 
tube. 

The obtained results I found in both experiments?  

The evoked motion patterns are exactly identical to what I could predict out 
of the theory I have presented last year on this List. 

The two sheets of paper are not at all moving in outward direction as was 
suggested. They are moving in opposite direction, so towards the core line 
of the alternating flow. And under a steady alternating stimulus (with 
constant amplitude) they both do that with a stationary deflection on which 
an alternating deflection is superposed with doubled frequency.
This indicates that both sheets experience the influence of an alternating 
and in average lower pressure evoked in the space between the two sheets.    

The tube experiment also shows that the membrane in the wall is always 
moving inwards ? so towards the core line of the tube. And superposed on a 
constant deflection inwards the membrane also deflects periodically with 
double frequency related to the original stimulus frequency.

Without any doubt this is indicating that at least squaring of the input 
stimulus plays a dominating role.

[Note: To make it even more convincing for everyone I will place a video 
registration of these experiments fairly soon on internet, like Walter Lewin 
does with his physics courses.] 

For now the only clear and firm conclusion I can draw is that the 
suggestions on this item of Dick Lion and others are wrong. The medium in 
the tube is moving as a whole. And therefore these experimental results, in 
combination with the theoretical solution of the non-stationary Bernoulli 
equation, are one of the reasons that the transmission line concept cannot 
play a role in it either. 

The second reason for rejecting the traveling wave concept is the following:

I also have studied the different possibilities for ?traveling waves? in 
literature. And then especially I have looked at the conditions, parameters 
and geometrical dimensions under which such waves can exist.

In short (you don?t need expensive literature retrievals, because you can 
read a summary of the possible wave forms in Wikipedia) we can state that 
there are three forms to distinguish:

1.	Rayleigh waves 

Rayleigh waves are a type of surface acoustic waves which travel on solid 
materials. 
The typical speed of these waves is slightly less than that of so-called 
shear waves. And it is by a factor (dependent on the elastic constants) 
given by the bulk material. This speed is of the order of 2?5 km/s.
For a sound signal with a 1000 Hz frequency this means that the minimal 
wavelength is approximately 2 meter. While the BM has a length of 
approximately 35 millimeter, it is impossible to make a realistic 
combination for application in the cochlea.
Besides that Rayleigh waves are surface waves where the thickness of the 
material must be relatively high related to the concerned wavelength. 
With a fraction of a millimeter thickness for the BM you can forget that 
this type of wave can play a role in the BM vibrations.

2.	Love waves

In the field of elastodynamics, Love waves, named after A. E. H. Love, are 
described as horizontally polarized shear waves guided by an elastic layer, 
which is "welded" to an elastic half space (so a very thick part of bulk 
material) on one side while bordering a vacuum on the other side. In 
literature can be found that the wavelength of these waves is relatively 
longer than that of Rayleigh waves.
And also these conditions and parameters are nowhere found in the cochlear 
partition. 

3.	Lamb waves

Lamb waves propagate in solid plates. They are elastic waves whose particle 
motion lies in the plane that contains the direction of wave propagation and 
the plate normal (the direction perpendicular to the plate). In 1917, the 
English mathematician Horace Lamb published his classic analysis and 
description of acoustic waves of this type.
The wave propagation velocities of the two possible modes in Lamb waves are 
comparable with that of the Rayleigh wave. And therefore they also don?t 
provide for a possible application in the traveling wave description inside 
the cochlea. 
In other words: we also cannot make a realistic fit with Lamb waves inside 
the cochlea.

Of course everybody can persist in believing that until now registered 
auditory experimental results justify the formulated hypothesis that such 
types of waves can exist in the cochlea. Then however you are forced to 
answer the following question:

On what underlying physics grounds is it possible that material quantities 
and acoustic process parameters inside the cochlea can be altered in such a 
way that as a result the wavelength of 1.5 meter for a 1000 Hz stimulus in 
bulk perilymph fluid can be altered in less than 1.5 millimeter?

As can be seen from the Rayleigh, Love and Lamb waves the circumstances and 
material properties cannot provide for a scaling factor better than 0.5 from 
bulk material sound velocity to the concerned type of wave.
Be aware that inside the cochlea a scaling factor of 0.001 or even smaller 
will have to be possible. This can be considered as completely impossible.  

What remains is that just as I stated before:

The described non-stationary Bernoulli effect, that provides for the sound 
energy stimulus everywhere in front of the BM, is driving the BM vibrations. 

And dear Randy this last statement above is my answer to your following 
remark:

** I have always wondered about what drives BM vibrations **

It is the everywhere present sound energy stimulus that drives the BM.

My following contribution will show the implication of all this for the rest 
of your request.



Kind regards

Willem Heerens