Subject: Re: Wave reflection. From: Mark Jurrens <m_jurrens@xxxxxxxx> Date: Fri, 11 Aug 2006 09:07:19 -0400--_fb762f4e-3124-40ad-a79b-6e321b89b7da_ Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Hi all, =20 This is very interesting stuff. I know a few of you gentlemen may wonder w= ho I am, my name is Mark, I am a beginning college student that is interest= ed in the basic cognitive mechanisms behind hearing internalization such as= storage, processing, and retrieval. I am also interested in what grants th= e brain(Mine that I have noticed so far) the ability to apply (at will) env= ironmental/modifying effects such as echo effects, octave adjustments, voic= e recognition/synthesis, etc. I have a keen interest in how the brain works= at the cognitive level and have created a few "Functional block diagrams= =94 of my own on how I interpret thought "I/O" using cognitive models of th= e brain as well as comparing them to the physical sub-processing areas.=20 =20 This mailing list may be a bit advanced for me, so I have been mostly just = reading these e-mails so that I would not say anything uneducated. But I am= somewhat familiar with psychology and cognition. If you believe me to be = misguided, I would be interested in pursuing further knowledge that perhaps= you may be able to lead me too elsewhere. However, at times, I am able to= relate to subject material such as the document mentioned below. I say the= se things, as I have received a notice requesting that I remove myself from= this mailing list most likely for lack of contribution. Thanks for your ti= me in advance, =20 Mark J. =20 ----- Original Message -----=20 From: "Richard F. Lyon" <DickLyon@xxxxxxxx> To: <AUDITORY@xxxxxxxx> Sent: Thursday, August 10, 2006 8:07 PM Subject: Re: Wave reflection. If this WKB validity issue matters to you, you better check out the appendi= x to Lloyd Watts's JASA paper (L. Watts, "The Mode-Coupling Liouville-Green= Approximation for a two-dimensional Cochlear Model", Journal of the Acoust= ical Society of America, vol. 108, no. 5, pp. 2266-2271, Nov., 2000), which= you can find linked here:http://www.lloydwatts.com/cochlea.shtmlHe says th= e usual criterion is only "first order" correct, and that in fact the WKB s= olution remains valid to much smaller k values (longer wavelengths) than it= suggests; so the long-wave solution is OK near the base, where this criter= ion says it should not be.He also shows what goes wrong past resonance, and= how to fix it.DickAt 8:20 PM +0200 8/10/06, reinifrosch@xxxxxxxx wrote:>= Hello again !>>I just found a good introductory treatment on nearly>reflect= ion-free waves, in the book "Physics of Waves">by W. C. Elmore and M. A. He= ald (Dover, New York, 1969).>In their section 9.1, they show that the WKB (= Wentzel, Kramers,>Brillouin) approximation is reflection-free, and that it = is>accurate if the local wavelength lambda obeys the following>inequality:= >>(d lambda / dx)^2 << 32 pi^2 . [their equation (9.1.15)] >>The corres= ponding inequality for the local wave number k is:>>k^-4 * (dk / dx)^2 << 8= .>>Reinhart Frosch.>>>>>>Reinhart Frosch,>Dr. phil. nat.,>r. PSI and ETH Z= urich,>Sommerhaldenstr. 5B,>CH-5200 Brugg.>Phone: 0041 56 441 77 72.>Mobile= : 0041 79 754 30 32.>E-mail: reinifrosch@xxxxxxxx .= --_fb762f4e-3124-40ad-a79b-6e321b89b7da_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable <html>=0A= <head>=0A= <style>=0A= P=0A= {=0A= margin:0px;=0A= padding:0px=0A= }=0A= body=0A= {=0A= FONT-SIZE: 10pt;=0A= FONT-FAMILY:Tahoma=0A= }=0A= </style>=0A= </head>=0A= <body><DIV>Hi all,</DIV> <DIV> </DIV> <DIV> This is very interesting stuff. I know a few of you gentlemen ma= y wonder who I am, my name is Mark, I am a beginning college student that i= s interested in the basic cognitive mechanisms behind hearing internal= ization such as storage, processing, and retrieval. I am also interest= ed in what grants the brain(Mine that I have noticed so far) = ;the ability to apply (at will) environmental/modifying effects such a= s echo effects, octave adjustments, voice recognition/synthesis, etc. = I have a keen interest in how the brain works at the cognitive level a= nd have created a few "Functional block diagrams=94 of my own on how I= interpret thought "I/O" using cognitive models of the brain as well as com= paring them to the physical sub-processing areas. </DIV> <DIV> </DIV> <P style=3D"MARGIN-BOTTOM: 0in">This mailing list may be a bit advanced for= me, so I have been mostly just reading these e-mails so that I would = not say anything uneducated. But I am somewhat familiar with psycholog= y and cognition. If you believe me to be misguided, I would be intere= sted in pursuing further knowledge that perhaps you may be able to lea= d me too elsewhere. However, at times, I am able to relate to su= bject material such as the document mentioned below. I say these things, as= I have received a notice requesting that I remove myself from this mailing= list most likely for lack of contribution. Thanks for your time in advance= ,</P> <P style=3D"MARGIN-BOTTOM: 0in"> </P> <P style=3D"MARGIN-BOTTOM: 0in">Mark J.</P> <P style=3D"MARGIN-BOTTOM: 0in"> </P> <DIV>----- Original Message -----=20 <DIV>From: "Richard F. Lyon" <<A href=3D"mailto:DickLyon@xxxxxxxx"><U><FO= NT color=3D#0000ff>DickLyon@xxxxxxxx</FONT></U></A>></DIV> <DIV>To: <<A href=3D"mailto:AUDITORY@xxxxxxxx"><U><FONT color=3D#= 800080>AUDITORY@xxxxxxxx</FONT></U></A>></DIV> <DIV>Sent: Thursday, August 10, 2006 8:07 PM</DIV> <DIV>Subject: Re: Wave reflection.</DIV></DIV> <DIV><BR></DIV>If this WKB validity issue matters to you, you <BR>better ch= eck out the appendix to Lloyd Watts's <BR>JASA paper (L. Watts, "The Mode-C= oupling <BR>Liouville-Green Approximation for a <BR>two-dimensional Cochlea= r Model", Journal of the <BR>Acoustical Society of America, vol. 108, no. 5= , <BR>pp. 2266-2271, Nov., 2000), which you can find <BR>linked here:<BR><A= href=3D"http://www.lloydwatts.com/cochlea.shtml"><U><FONT color=3D#0000ff>= http://www.lloydwatts.com/cochlea.shtml</FONT></U></A><BR>He says the usual= criterion is only "first order" <BR>correct, and that in fact the WKB solu= tion <BR>remains valid to much smaller k values (longer <BR>wavelengths) th= an it suggests; so the long-wave <BR>solution is OK near the base, where th= is <BR>criterion says it should not be.<BR>He also shows what goes wrong pa= st resonance, and how to fix it.<BR><BR>Dick<BR><BR>At 8:20 PM +0200 8/10/0= 6, <A href=3D"mailto:reinifrosch@xxxxxxxx"><U><FONT color=3D#0000ff>reini= frosch@xxxxxxxx</FONT></U></A> wrote:<BR>>Hello again !<BR>><BR>>= ;I just found a good introductory treatment on nearly<BR>>reflection-fre= e waves, in the book "Physics of Waves"<BR>>by W. C. Elmore and M. A. He= ald (Dover, New York, 1969).<BR>>In their section 9.1, they show that th= e WKB (Wentzel, Kramers,<BR>>Brillouin) approximation is reflection-free= , and that it is<BR>>accurate if the local wavelength lambda obeys= the following<BR>>inequality:<BR>><BR>>(d lambda / dx)^2 <<= 32 pi^2 . [their equation (9.1.15)] <BR>><BR>&g= t;The corresponding inequality for the local wave number k is:<BR>><BR>&= gt;k^-4 * (dk / dx)^2 << 8 .<BR>><BR>>Reinhart Frosch.<BR>><= BR>><BR>><BR>><BR>><BR>>Reinhart Frosch,<BR>>Dr. phil. na= t.,<BR>>r. PSI and ETH Zurich,<BR>>Sommerhaldenstr. 5B,<BR>>CH-520= 0 Brugg.<BR>>Phone: 0041 56 441 77 72.<BR>>Mobile: 0041 79 754 30 32.= <BR>>E-mail: <A href=3D"mailto:reinifrosch@xxxxxxxx"><U><FONT color=3D= #0000ff>reinifrosch@xxxxxxxx</FONT></U></A> .<BR></body>=0A= </html>= --_fb762f4e-3124-40ad-a79b-6e321b89b7da_--