Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post")) From: Peter van Hengel <pwj.vanhengel@xxxxxxxx> Date: Tue, 1 Nov 2011 15:09:06 +0100 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--00163642669308379204b0ace63e Content-Type: text/plain; charset=ISO-8859-1 Dear Dick, I want to express my complete agreement with your response and have little to add. Just the remark that the statement made by dr Heerens that transmission line models would be specifically designed to support the traveling wave is incorrect. Such models are based on physics and derived from the Navier-Stokes equations. No assumptions about possible or impossible wave propagation are made in the derivation of the equations of motion, not in the numerical implementation. Only the compressibility of the fluid is generally - not always - neglected, which leads to an infinite velocity of compression waves. Kind regards, Peter 2011/10/31 Richard F. Lyon <DickLyon@xxxxxxxx> > At 4:57 PM -0400 10/31/11, Willem Christiaan Heerens wrote: > >> ... I really must remind you to the fact that a mechanical vibration -- >> and the sound stimulus is such a vibration -- in a fluid, or in this case >> water like perilymph, will always propagate with the speed of sound, which >> has typically here the value of 1500 m/s. That is just one of those >> constraints dictated by general physics. >> > > Willem, > > No, not "always"; that 1500 m/s wave mode is for longitudinal pressure > waves only. Your conception of "general physics" needs a slight extension > to cover other types of waves. Then the problem won't be so > over-constrained. > > In the ear, the stapes doesn't couple much energy into this fast > pressure-wave mode. A much slower propagating vibration mode is involved > in the cochlear traveling waves that use the compliance of the basilar > membrane, as opposed to compression of the fluid, as the displacement-based > restoring force that leads to the wave equations. This mode has a very > different form, doesn't depend on fluid compressibility, requires a > membrane with motion in a suitable symmetry across it, etc. This is what > the physics describes, and what the models model. > > Gravity waves on water are a related, but different, example of mechanical > vibrations that propagate much more slowly than 1500 m/s. These modes use > gravity as the restoring force, and can be put into analogy with what the > membrane does in the cochlea (though it's not such a close analogy as to > give the same wave equations). > > Of course, until one acknowledges the basic physics of waves in > incompressible fluids, as described by Lamb and Rayleigh and others over a > hundred years ago, it will not be possible to converge on an understanding > of cochlear models and their traveling waves. > > The physics and math are pretty simple, relying only on f=ma for fluid > elements, and conservation of volume for incompressibility, and something > to make a restoring force. To get waves, you need something to hold > potential energy and push back against displacment, to trade that energy > against the kinetic energy of moving fluid. Fluid compression is one such > mechanism, but there are others that your approach is ignoring. This is > what the membrane is about: springiness, or compliance. The membrane > compliance has been measured, and the measurements fit the physical models > and the observed wave speeds. > > Adding some compressibility to the model is also possible, and is needed > to get that fast pressure mode as well, which I agree is involved in > getting the round window to be pushed out when the oval window is pushed > in. But that can be approximated well enough with incompressible and > infinite-velocity pressure waves, since the wavelengths are so long, as you > point out. These pressure waves don't create any differential pressures > around the basilar membrane, and have negligible associated displacements > and velocities everywhere (even at the windows), compared to the > traveling-wave modes, so they are typically ignored in the discussion of > cochlear hydrodynamics, where the motions are what we care about. > > Sorry to be so long-winded. > > Dick > --00163642669308379204b0ace63e Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <div>Dear Dick,</div> <div>=A0</div> <div>I want to express my complete agreement with your response and have=A0= little to add.</div> <div>Just the remark that the statement made by dr Heerens that transmissio= n line models would be specifically designed to support the traveling wave = is incorrect. Such models are based on physics and derived from the Navier-= Stokes equations. No assumptions about possible or impossible wave propagat= ion are made in the derivation of the equations of motion, not in the numer= ical implementation. Only the compressibility of the fluid is generally - n= ot always - neglected, which leads to an infinite velocity of compression w= aves.<br> </div> <div>Kind regards,</div> <div>Peter<br></div> <div class=3D"gmail_quote">2011/10/31 Richard F. Lyon <span dir=3D"ltr"><= ;<a href=3D"mailto:DickLyon@xxxxxxxx">DickLyon@xxxxxxxx</a>></span><br> <blockquote style=3D"BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex= ; PADDING-LEFT: 1ex" class=3D"gmail_quote">At 4:57 PM -0400 10/31/11, Wille= m Christiaan Heerens wrote:<br> <blockquote style=3D"BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex= ; PADDING-LEFT: 1ex" class=3D"gmail_quote">... I really must remind you to = the fact that a mechanical vibration -- and the sound stimulus is such a vi= bration -- in a fluid, or in this case water like perilymph, will always pr= opagate with the speed of sound, which has typically here the value of 1500= m/s. That is just one of those constraints dictated by general physics.<br= > </blockquote><br>Willem,<br><br>No, not "always"; that 1500 m/s w= ave mode is for longitudinal pressure waves only. =A0Your conception of &qu= ot;general physics" needs a slight extension to cover other types of w= aves. =A0Then the problem won't be so over-constrained.<br> <br>In the ear, the stapes doesn't couple much energy into this fast pr= essure-wave mode. =A0A much slower propagating vibration mode is involved i= n the cochlear traveling waves that use the compliance of the basilar membr= ane, as opposed to compression of the fluid, as the displacement-based rest= oring force that leads to the wave equations. This mode has a very differen= t form, doesn't depend on fluid compressibility, requires a membrane wi= th motion in a suitable symmetry across it, etc. =A0This is what the physic= s describes, and what the models model.<br> <br>Gravity waves on water are a related, but different, example of mechani= cal vibrations that propagate much more slowly than 1500 m/s. These modes u= se gravity as the restoring force, and can be put into analogy with what th= e membrane does in the cochlea (though it's not such a close analogy as= to give the same wave equations).<br> <br>Of course, until one acknowledges the basic physics of waves in incompr= essible fluids, as described by Lamb and Rayleigh and others over a hundred= years ago, it will not be possible to converge on an understanding of coch= lear models and their traveling waves.<br> <br>The physics and math are pretty simple, relying only on f=3Dma for flui= d elements, and conservation of volume for incompressibility, and something= to make a restoring force. =A0To get waves, you need something to hold pot= ential energy and push back against displacment, to trade that energy again= st the kinetic energy of moving fluid. Fluid compression is one such mechan= ism, but there are others that your approach is ignoring. =A0This is what t= he membrane is about: springiness, or compliance. =A0The membrane complianc= e has been measured, and the measurements fit the physical models and the o= bserved wave speeds.<br> <br>Adding some compressibility to the model is also possible, and is neede= d to get that fast pressure mode as well, which I agree is involved in gett= ing the round window to be pushed out when the oval window is pushed in. = =A0But that can be approximated well enough with incompressible and infinit= e-velocity pressure waves, since the wavelengths are so long, as you point = out. =A0These pressure waves don't create any differential pressures ar= ound the basilar membrane, and have negligible associated displacements and= velocities everywhere (even at the windows), compared to the traveling-wav= e modes, so they are typically ignored in the discussion of cochlear hydrod= ynamics, where the motions are what we care about.<br> <br>Sorry to be so long-winded.<br><br>Dick<br></blockquote></div><br> --00163642669308379204b0ace63e--