Re: Laws of physics and old history; BM stiffness. ("reinifrosch@xxxxxxxx" )


Subject: Re: Laws of physics and old history; BM stiffness.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Fri, 11 Nov 2011 11:35:22 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

------=_Part_2020_26794625.1321011322881 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Hello! The following is a reaction to an earlier post of this thread: As already posted some years ago, it appears possible to me that the stiffn= ess S [Newtons per m^3] of the mammalian cochlear basilar membrane (BM) dec= reases by several orders of magnitude from base to apex. If the elements of= the BM are treated as elastic beams, then the following formula for S is o= btained: S =3D n * Y * (delta-z)^3 / w^4, where delta-z is the beam thickness, w is the beam length (equal to the BM = width), and Y is Young's modulus of the beam material (elasticity modulus, = Newtons per m^2); the integer n depends on the way in which the beams are f= ixed, at their ends, to the walls of the cochlear channel. If the beams are= clamped, then n =3D 60, if not, then n =3D 10. Fig. 11-73 of von Bekesy's book "Experiments in Hearing" (1960) yields a hu= man BM stiffness decrease of only two orders of magnitude from base to apex= . Has that experiment been re-done?=20 Reinhart Frosch, Dr. phil. nat., CH-5200 Brugg. reinifrosch@xxxxxxxx . ----Urspr=C3=BCngliche Nachricht---- Von: rsran@xxxxxxxx Datum: 09.11.2011 20:17 An: <AUDITORY@xxxxxxxx> Betreff: Re: Laws of physics and old history (A new paradigm?(On pitch and = periodicity (was &amp;quot;correction to post&amp;quot;))) ------=_Part_2020_26794625.1321011322881 Content-Type: text/html;charset="UTF-8" Content-Transfer-Encoding: quoted-printable <html><head><style type=3D'text/css'> <!-- div.bwmail { background-color:#ffffff; font-family: Trebuchet MS,Arial,Helv= etica, sans-serif; font-size: small; margin:0; padding:0;} div.bwmail p { margin:0; padding:0; } div.bwmail table { font-family: Trebuchet MS,Arial,Helvetica, sans-serif; f= ont-size: small; } div.bwmail li { margin:0; padding:0; } --> </style> </head><body><div class=3D'bwmail'><P><FONT size=3D2>Hello!</FONT></P> <P><FONT size=3D2>The following is a reaction to an earlier post of this th= read:</FONT></P> <P><FONT size=3D2>As already posted some years ago, it appears possible to = me that the stiffness S [Newtons per m^3] of the mammalian cochlear basilar= &nbsp;membrane (BM) decreases&nbsp;by several orders of magnitude from base= to apex. If the elements of the BM are treated as elastic beams, then the = following formula for S is obtained:</FONT></P> <P><FONT size=3D2>S =3D n * Y * (delta-z)^3 / w^4,</FONT></P> <P><FONT size=3D2>where delta-z is the beam thickness, w is the beam length= (equal to the BM width), and Y is Young's modulus of the beam material (el= asticity modulus, Newtons per m^2); the integer n&nbsp;depends on the way i= n which the beams are fixed, at their ends,&nbsp;to the walls&nbsp;of the c= ochlear channel. If the beams are clamped, then n =3D 60, if not, then n = =3D 10.</FONT></P> <P><FONT size=3D2>Fig. 11-73 of von Bekesy's book "Experiments in Hearing" = (1960) yields a human BM stiffness decrease of only two orders of magnitude= &nbsp;from base to apex.&nbsp;Has that experiment been re-done?&nbsp;</FONT= ></P> <P><BR><FONT size=3D2>Reinhart Frosch,<BR>Dr. phil. nat.,<BR>CH-5200 Brugg.= <BR>reinifrosch@xxxxxxxx .</FONT><BR><BR></P> <BLOCKQUOTE><FONT size=3D2>----Urspr=C3=BCngliche Nachricht----<BR>Von: rsr= an@xxxxxxxx<BR>Datum: 09.11.2011 20:17<BR>An: &lt;AUDITORY@xxxxxxxx= CA&gt;<BR>Betreff: Re: Laws of physics and old history (A new paradigm?(On = pitch and periodicity (was &amp;quot;correction to post&amp;quot;)))<BR><BR= ></FONT></BLOCKQUOTE></div></body></html> ------=_Part_2020_26794625.1321011322881--


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