Calculating sound speed?
Dirk Van de moortel
I'll post it again...
I've often wondered whether and under which circumstances
sound speed could be theoretically calculated ("post-dicted")
from light speed and known, guessed or idealized material
properties like for instance crystal structure.
After all, sound can be interpreted as a wave travelling through
a medium of atoms, so a disturbance travelling from one atom
to a neighbouring atom should take place at light speed.
Someone *must* have thought about and worked on this
before.
Any idea?
Dirk Vdm
Jean-Christophe MATHAE
dans le message de news: lvVA9.2489$Ti2...@afrodite.telenet-ops.be...
> After all, sound can be interpreted as a wave travelling through
> a medium of atoms, so a disturbance travelling from one atom
> to a neighbouring atom should take place at light speed.
The electro-magnetic force does travel at the speed of light (in that
medium), but not the atoms of course.
Like in an electric motor: the magnetic flux travels at the speed of light
but the motor turns MUCH slower.
--
Jean-Christophe MATHAE
12, impasse Jean-Pierre Blanchard
31400 Toulouse
France
Dirk Van de moortel
"Jean-Christophe MATHAE" <jch.m...@free.fr> wrote in message news:3dd4356d$0$23002$626a...@news.free.fr...
> "Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> a écrit
> dans le message de news: lvVA9.2489$Ti2...@afrodite.telenet-ops.be...
> > After all, sound can be interpreted as a wave travelling through
> > a medium of atoms, so a disturbance travelling from one atom
> > to a neighbouring atom should take place at light speed.
>
> The electro-magnetic force does travel at the speed of light (in that
> medium), but not the atoms of course.
Of course :-)
> Like in an electric motor: the magnetic flux travels at the speed of light
> but the motor turns MUCH slower.
Of course again.
My question was whether and under which circumstances
one would be able to calculate *how* much slower, as a
*function* of the speed of light and the properties of the
material.
I know this is a real tough problem. I am wondering how
tough and whether someone knows whether work has
been done on it.
Dirk Vdm
Russell Blackadar
[snip]
> My question was whether and under which circumstances
> one would be able to calculate *how* much slower, as a
> *function* of the speed of light and the properties of the
> material.
I am not at all familiar with stellar interiors, which might
be different, but for ordinary materials I would say that
"the [other] properties" will always dominate the function
you are proposing, and that the "speed of light" part is
negligible. What matters to sound is how quickly the massive
atomic nuclei respond to the field changes in their vicinity,
not how quickly those field changes propagate between the atoms;
the latter speed is effectively infinite in comparison and thus
of no import whatsoever to the overall rate.
No doubt the speed of light is *correlated* with speed of
sound in certain kinds of materials, but that doesn't imply
any direct causal relationship between the two.
Gregory L. Hansen
Maybe I misunderstand the question, but speed of sound in crystals is
something solid-state physicists worked on very early. And it works well
in the non-relativistic approach, so I don't think there'd be Lorentz
transformation issues. Maybe you could relate the strength of
electromagnetic interactions to the speed of light, surely a stronger
field would make the crystal "stiffer" and the sound faster.
It's a good thing you just asked for ideas, not answers.
--
"A nice adaptation of conditions will make almost any hypothesis agree
with the phenomena. This will please the imagination but does not advance
our knowledge." -- J. Black, 1803.
Jonathan E. Hardis
moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
Sound speed has nothing to do with light speed.
Sound is a mechanical wave. You can calculate sound speed in a material
by knowing the mechanical properties of the material.
A catalog of *which* properties gets complicated very quickly. There are
two kinds of sound waves, longitudinal (compressive, like sound in the
air), and transverse (like sound waves travling down a plucked string).
There are also issues in solid mechanics where a material doesn't deform
in the same direction as the applied force (stress). I believe "Young's
Modulus" or "Elastic Tensor" covers this, but I really don't remember.
However, in general, you are looking for two properties: (1) some sort of
"stiffness" measure (how much or little a material deforms under applied
force), and (2) some sort of "inertial" measure, such as material density.
One way of interpreting your question, then, is: can one compute a
material's "stiffness" and its "density" from first principles? Well,
there's nothing that prevents it. However, computational complexity would
be a limiting factor for many materials. The main ingredients in the
computational soup would be the basic principles of quantum mechanics and
the charges and masses of the stuff that make up the material (electrons
and atomic nuclii).
Your "jump to light speed" is misplaced intuition, but I can't give you an
obviously satisfactory answer. Let's try this, though. The absolute
simplest mechanical vibration (sound wave) I can think of is a simple
pendulum. [The "stiffness" measure comes gravational pull, and the
"inertial" measure is the pendulum's mass.] As a pendulum swings back and
forth, all the bits and pieces in some sense communicate with each other
at the speed of light. But, so what?
- Jonathan
Old Man
message news:lvVA9.2489$Ti2...@afrodite.telenet-ops.be...
There is no reasonable analogy between EM waves and sound
waves. EM waves self-propagate through free space, and sound
waves propagate as disturbances in a necessary ponderable
medium. The speed of propagation of sound, v, depends upon
the density, rho, and the bulk modulus of elasticity of the material
medium, B, such that v = sqrt(B / rho). The oscillating electric
and magnetic fields of an EM wave have direction transverse to
the direction of wave propagation, and the alternating pressure
gradients of a sound wave are longitudinal to the direction of
wave propagation. [Old Man]
Dirk Van de moortel
"Jonathan E. Hardis" <jha...@tcs.wap.org> wrote in message news:jhardis-1411...@dialup17.wap.org...
> In article <lvVA9.2489$Ti2...@afrodite.telenet-ops.be>, "Dirk Van de
> moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
> > Asked this yesterday but I'm afraid it got lost in some noise :-(
> > I'll post it again...
> >
> > I've often wondered whether and under which circumstances
> > sound speed could be theoretically calculated ("post-dicted")
> > from light speed and known, guessed or idealized material
> > properties like for instance crystal structure.
> > After all, sound can be interpreted as a wave travelling through
> > a medium of atoms, so a disturbance travelling from one atom
> > to a neighbouring atom should take place at light speed.
> > Someone *must* have thought about and worked on this
> > before.
> > Any idea?
>
> Sound speed has nothing to do with light speed.
Suppose that light speed would be 10000 m/sec.
Surely I can imagine that sound speed in steel would not be
6000 m/sec then.
I know, this is a ridiculous example, but what I'm aiming at,
is that there could be *some* connection. Most probably
not a simple linear one, but something.
>
> Sound is a mechanical wave. You can calculate sound speed in a material
> by knowing the mechanical properties of the material.
>
> A catalog of *which* properties gets complicated very quickly. There are
> two kinds of sound waves, longitudinal (compressive, like sound in the
> air), and transverse (like sound waves travling down a plucked string).
> There are also issues in solid mechanics where a material doesn't deform
> in the same direction as the applied force (stress). I believe "Young's
> Modulus" or "Elastic Tensor" covers this, but I really don't remember.
> However, in general, you are looking for two properties: (1) some sort of
> "stiffness" measure (how much or little a material deforms under applied
> force), and (2) some sort of "inertial" measure, such as material density.
>
> One way of interpreting your question, then, is: can one compute a
> material's "stiffness" and its "density" from first principles? Well,
> there's nothing that prevents it. However, computational complexity would
> be a limiting factor for many materials.
Of course, for many (and probably for most) materials.
My question.is about for which (possibly idealized) materials,
if any, it *would* be possible to have a detailed calculation
that has c the final result - see below.
> The main ingredients in the
> computational soup would be the basic principles of quantum mechanics and
> the charges and masses of the stuff that make up the material (electrons
> and atomic nuclii).
Oh yes, quite indeed.
>
> Your "jump to light speed" is misplaced intuition, but I can't give you an
> obviously satisfactory answer. Let's try this, though. The absolute
> simplest mechanical vibration (sound wave) I can think of is a simple
> pendulum. [The "stiffness" measure comes gravational pull, and the
> "inertial" measure is the pendulum's mass.] As a pendulum swings back and
> forth, all the bits and pieces in some sense communicate with each other
> at the speed of light. But, so what?
The pendulum seems a bit crude as an example of the simplest
mechanical vibration. As a simple example I have in mind a system
of a chain of N atoms, where one atom is severely disturbed at
one end. How long does it take for the wave to propagate through
the chain?
No doubt, this is pretty advanced QM :-)
I'm not looking for an answer to this specific question... just whether
it might have been treated before somewhere...
>
> - Jonathan
Thanks for replying already - to all!
Dirk Vdm
Randy Poe
> There is no reasonable analogy between EM waves and sound
> waves. EM waves self-propagate through free space, and sound
> waves propagate as disturbances in a necessary ponderable
> medium. The speed of propagation of sound, v, depends upon
> the density, rho, and the bulk modulus of elasticity of the material
> medium, B, such that v = sqrt(B / rho).
An add-on to my previous post.
The "elastic" properties are consequences of the
quantum mechanics of the bonds. I wondered out loud
if you could use QM to derive these properties. Now
I'm convinced that (in principle) you could. The
restoring force in an elastic structure is the derivative
of the potential energy as a function of distance.
The QM approach would be to figure out how the
ground state energy changes with deformation.
The derivative of that thing will tell you your
spring constant.
- Randy
Randy Poe
> In article <lvVA9.2489$Ti2...@afrodite.telenet-ops.be>, "Dirk Van de
> moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
>
>>Asked this yesterday but I'm afraid it got lost in some noise :-(
>>I'll post it again...
>>
>>I've often wondered whether and under which circumstances
>>sound speed could be theoretically calculated ("post-dicted")
>>from light speed and known, guessed or idealized material
>>properties like for instance crystal structure.
>>After all, sound can be interpreted as a wave travelling through
>>a medium of atoms, so a disturbance travelling from one atom
>>to a neighbouring atom should take place at light speed.
>>Someone *must* have thought about and worked on this
>>before.
>>Any idea?
>
>
> Sound speed has nothing to do with light speed.
>
> Sound is a mechanical wave. You can calculate sound speed in a material
> by knowing the mechanical properties of the material.
I understand Dirk's question. He is saying that since
"mechanical" interactions are electromagnetic at the
molecular level, can the mechanical properties of a solid
be deduced entirely by electromagnetic theory.
I took a course in solid state physics long ago, and
I don't remember the answer to this. It seems to me
it was a semi-classical approach, using mostly classical
physics but ultimately relying on parameters which were
given by the quantum nature of the interactions.
I think the real answer would lie in quantum mechanics,
not electromagnetics. You're asking what happens to
chemical bonds when deformed. Can you use QM to deduce
the mechanical properties of a solid?
- Randy
Edward Green
Just some thoughts, Dirk.
What is a calculation of sound speed based on? Bulk elastic constants
-- right? Ok. Now, ab initio, how would you go about calculating
bulk elastic constants? Well probably in some way you would attempt
to solve a Shroedinger equation in some quasi-static approximation to
find interatomic potentials. Ok. Now, what factors does the
Shroedinger equation account for? Well for one thing, it takes as
input a potential function on electrons. Ok (OK? :-). And this
potential function arises from what? From the EM field.
So, in a sense, in the normal route of prediction of sound speed
starting ab initio, the EM field is accounted for early on --
implicity there is your "speed of light", or layer of electromagnetic
interaction (I'm reminded of the 7 layer model of networks,
unavoidably).
Some complications -- I'm not sure the ordinary Schroedinger equation
effectively accounts for propagation in the EM field. It only uses a
position based potential, so may in effect assume c is infinite.
Since it seems possible to get reasonable results this way, this may
mean that sound speed doesn't really depend too critically on the
value of c directly.
Another thing, in any discussion of wave propagation we probably have
to have a side discussion about the speed of signal propagation --
phase vs. group vs. information and all that jazz. I think in an
analytic universe essentially all disturbances must be propagated
instantaneously to infinity -- in a very limited sense of "propagate"
-- since altering a small neighborhood of an analytic function alters
the entire function out to infinity ... there are no "surprises" in
analytic functions.
Anyway ... I think bottom line is your program is effectively already
carried out, simply in a form you may not recognize.
Ed
Dirk Van de moortel
"Edward Green" <null...@aol.com> wrote in message news:2a0cceff.02111...@posting.google.com...
good thoughts so far :-)
>
> Some complications -- I'm not sure the ordinary Schroedinger equation
> effectively accounts for propagation in the EM field. It only uses a
> position based potential, so may in effect assume c is infinite.
> Since it seems possible to get reasonable results this way, this may
> mean that sound speed doesn't really depend too critically on the
> value of c directly.
That would be a good point. If this is true, then I have a
clear answer to my question: it would be "no".
>
> Another thing, in any discussion of wave propagation we probably have
> to have a side discussion about the speed of signal propagation --
> phase vs. group vs. information and all that jazz. I think in an
> analytic universe essentially all disturbances must be propagated
> instantaneously to infinity -- in a very limited sense of "propagate"
> -- since altering a small neighborhood of an analytic function alters
> the entire function out to infinity ... there are no "surprises" in
> analytic functions.
aaarf.
>
> Anyway ... I think bottom line is your program is effectively already
> carried out, simply in a form you may not recognize.
Well, it's not really my program. I was more or less looking
for some article in some journal with some title like
"First principles calculation of sound speed in crystalline NaCl"
I guess it has not been done ;-)
Thanks, good thoughts!
Dirk Vdm
Gregory L. Hansen
Dirk Van de moortel <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>Well, it's not really my program. I was more or less looking
>for some article in some journal with some title like
>"First principles calculation of sound speed in crystalline NaCl"
>I guess it has not been done ;-)
That much has certainly been done, e.g. Kittel (1953), chapter 4. It's
what early solid state physics was all about--trying to calculate speed of
sound, specific heat, thermal and electrical conductivity, and other
properties from first principles.
That is, given the positions of the atoms in the crystal in the first
place. Calculating the arrangement of atoms in a crystal from first
principles is hard. But with new, faster computers, some companies are
designing new alloys from first principles and getting the properties they
want from the first batch.
Dirk Van de moortel
"Gregory L. Hansen" <glha...@steel.ucs.indiana.edu> wrote in message news:ar3jk4$f1d$1...@hood.uits.indiana.edu...
> In article <sSbB9.3411$Ti2...@afrodite.telenet-ops.be>,
> Dirk Van de moortel <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
> >Well, it's not really my program. I was more or less looking
> >for some article in some journal with some title like
> >"First principles calculation of sound speed in crystalline NaCl"
> >I guess it has not been done ;-)
>
> That much has certainly been done, e.g. Kittel (1953), chapter 4. It's
> what early solid state physics was all about--trying to calculate speed of
> sound, specific heat, thermal and electrical conductivity, and other
> properties from first principles.
Google reveals:
"Kittel, Charles: Introduction to Solid State Physics (1953)"
Since I don't have a Kittel near me, you don't by any chance
happen to spot c to be lurking somewhere in some of the final
expressions of these properties?
>
> That is, given the positions of the atoms in the crystal in the first
> place. Calculating the arrangement of atoms in a crystal from first
> principles is hard. But with new, faster computers, some companies are
> designing new alloys from first principles and getting the properties they
> want from the first batch.
We're getting somewhere :-)
Thanks,
Dirk Vdm
Gregory L. Hansen
Dirk Van de moortel <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
>"Gregory L. Hansen" <glha...@steel.ucs.indiana.edu> wrote in message
>news:ar3jk4$f1d$1...@hood.uits.indiana.edu...
>> In article <sSbB9.3411$Ti2...@afrodite.telenet-ops.be>,
>> Dirk Van de moortel <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>>
>> >Well, it's not really my program. I was more or less looking
>> >for some article in some journal with some title like
>> >"First principles calculation of sound speed in crystalline NaCl"
>> >I guess it has not been done ;-)
>>
>> That much has certainly been done, e.g. Kittel (1953), chapter 4. It's
>> what early solid state physics was all about--trying to calculate speed of
>> sound, specific heat, thermal and electrical conductivity, and other
>> properties from first principles.
>
>Google reveals:
> "Kittel, Charles: Introduction to Solid State Physics (1953)"
>Since I don't have a Kittel near me, you don't by any chance
>happen to spot c to be lurking somewhere in some of the final
>expressions of these properties?
I'm sure any solid state physics text would have the same stuff.
It's only there implicitly, in the strength of the interaction and the
fact that it's high enough to ignore relativistic effects. We have the
fine structure constant alpha=e^2/(hbar*c). If c were much smaller I
suppose an electric charge would be "worth" more; if c were half as large
then the electromagnetic interaction would be twice as strong? If the
masses of particles stay the same, that would speed up sound by a factor
of 2, or sqrt(2), something like that.
I think magnetic effects are generally ignored, but if c were much smaller
maybe the magnetic field strength would be of the order of the electric
field strength.
Dirk Van de moortel
"Gregory L. Hansen" <glha...@steel.ucs.indiana.edu> wrote in message news:ar3lqu$feh$1...@hood.uits.indiana.edu...
Next time I visit the university library, I'll skim through Kittel
and comparables.
Thanks for sharing thoughts, Gregory [and others!]
Dirk Vdm
Franz Heymann
> moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
> > Asked this yesterday but I'm afraid it got lost in some noise :-(
> > I'll post it again...
> >
> > I've often wondered whether and under which circumstances
> > sound speed could be theoretically calculated ("post-dicted")
> > from light speed and known, guessed or idealized material
> > properties like for instance crystal structure.
> > After all, sound can be interpreted as a wave travelling through
> > a medium of atoms, so a disturbance travelling from one atom
> > to a neighbouring atom should take place at light speed.
> > Someone *must* have thought about and worked on this
> > before.
> > Any idea?
>
> Sound speed has nothing to do with light speed.
>
> Sound is a mechanical wave. You can calculate sound speed in a
material
> by knowing the mechanical properties of the material.
You did not get deeply enough into Dirk's problem. Ultimately the
elastic properties of, say, a solid, are determined by electromagnetic
interactions between neighbouring atoms. And these electromagnetic
forces are propagated at the speed of light.
>
> A catalog of *which* properties gets complicated very quickly. There
are
> two kinds of sound waves, longitudinal (compressive, like sound in the
> air), and transverse (like sound waves travling down a plucked
string).
> There are also issues in solid mechanics where a material doesn't
deform
> in the same direction as the applied force (stress). I believe
"Young's
> Modulus" or "Elastic Tensor" covers this, but I really don't remember.
> However, in general, you are looking for two properties: (1) some
sort of
> "stiffness" measure (how much or little a material deforms under
applied
> force), and (2) some sort of "inertial" measure, such as material
density.
>
> One way of interpreting your question, then, is: can one compute a
> material's "stiffness" and its "density" from first principles?
Ah! you've got it!
> Well,
> there's nothing that prevents it. However, computational complexity
would
> be a limiting factor for many materials. The main ingredients in the
> computational soup would be the basic principles of quantum mechanics
and
> the charges and masses of the stuff that make up the material
(electrons
> and atomic nuclii).
>
> Your "jump to light speed" is misplaced intuition, but I can't give
you an
> obviously satisfactory answer. Let's try this, though. The absolute
> simplest mechanical vibration (sound wave) I can think of is a simple
> pendulum. [The "stiffness" measure comes gravational pull, and the
> "inertial" measure is the pendulum's mass.] As a pendulum swings back
and
> forth, all the bits and pieces in some sense communicate with each
other
> at the speed of light. But, so what?
In the end I think one has to agree with you. The mechanical motions
involved in a sound wave have speeds which are utterly negligible
compared with that of light, so that for practical purposes the EM
propagation part of the process is essentially instantaneous.
Franz Heymann
Old Man
news:ar32c...@enews1.newsguy.com...
Old Man thinks that sound speed in a real gas, say 4He, can be
predicted accurately at STP via the standard ideal gas model
without use of QM or referral to the speed of light. Because of
this, the speeds of sound and light are related, via the inter-
atomic electromagnetic forces, only very weakly through higher
order terms of an expansion in terms of (v_sound / c )^n.
[Old Man]
Ype
Dirk Van de moortel wrote:
> Asked this yesterday but I'm afraid it got lost in some noise :-(
> I'll post it again...
>
> I've often wondered whether and under which circumstances
> sound speed could be theoretically calculated ("post-dicted")
> from light speed and known, guessed or idealized material
> properties like for instance crystal structure.
When you heat some gas, speed of sound in the gas approaches some
speed below c. Maybe c divided by square-root of 2, or something like
that.
> After all, sound can be interpreted as a wave travelling through
> a medium of atoms, so a disturbance travelling from one atom
> to a neighbouring atom should take place at light speed.
This gives speed of sound = c. No?
I guess this is an infinitely weak sound.
When we define speed of sound, we let the sound travel an
infinite distance, then we ignore the infinely weak waves.
Well that sounds like a reasonable definition to me anyway.
Sam Wormley
>
>
> When you heat some gas, speed of sound in the gas approaches some
> speed below c. Maybe c divided by square-root of 2, or something like
> that.
>
See: http://scienceworld.wolfram.com/physics/SpeedofSound.html
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
For a more advanced treatment, see:
"Acoustic Fields and Waves in Solids, Vol I & II" by B.A. Auld, 2nd edition
(February 1990), Krieger Publishing Company; ISBN: 089874783X
"Ultrasonic Testing of Materials" by Josef Krautkramer, Herbert Krautkramer,
4th/revised edition (November 1990), Springer Verlag; ISBN: 0387512314