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Two-dimensional cochlear short-wave model.
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
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.
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,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .