Two-dimensional cochlear short-wave model. ("reinifrosch@xxxxxxxx" )

Subject: Two-dimensional cochlear short-wave model.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Sun, 3 Feb 2008 11:56:33 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Dear List Members,

In recent calculations of phases of distortion-products (DP's) and 
DP oto-acoustic emissions (DPOAE's) in mammalian cochleae I have 
obtained fairly good agreement with measured phases by means of the 
two-dimensional short-wave cochlear model; see, e.g., Eq. (23) of  
"Ranke revisited -- a simple short-wave cochlear model" by W. M. 
Siebert (1974), JASA 56, 594-600.

Here I would like to point out that according to my (hopefully 
correct) interpretation of this model the radius r of the 
approximately half-circle-shaped "wavy" liquid zones on both sides of 
the basilar membrane (BM) in the real cochlea depends on the BM 
width.

First case: 
Local wave number of travelling surface wave: 
k = 2pi / wavelength = 1000 m^-1;
thickness of liquid layers with significant water-particle motion 
(on circular trajectories): delta-z = 1/k = 1 mm;
BM-width: w = 0.1 mm; 
half-channel cross section: q_hc = 1 mm^2; 
therefore effective half-channel height H = q_hc / w = 10 mm;
short-wave condition is fulfilled: Hk = 10 >> 1;
cross section of wavy liquid zones: 
q_wz = w * delta-z  = 0.1 mm^2;
radius of half-circle-shaped wavy zone in real cochlea: 
r = sqrt(2q_wz / pi) = 0.25 mm.

Second case:
As first case, but w = 0.2 mm;
therefore H = 5 mm; Hk = 5 >> 1; 
short-wave condition is still fulfilled;
q_wz = 0.2 mm^2; r = 0.36 mm, greater than in first case.

With best wishes,

Reinhart Frosch. 

Reinhart Frosch,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Sommerhaldenstr. 5B,
CH-5200 Brugg.
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxx .