| Topic: |
Science > Physics |
| User: |
"Cheng Cosine" |
| Date: |
03 Jan 2005 12:09:59 AM |
| Object: |
? phys meaning of partial wave soln |
Hi:
The general soln of a linear scalar wave eqn can be expressed as
f(x+c*t)+f(x-c*t).
The phys meaning of f(x+c*t) is a wave moving to the left while f(x-c*t) is
moving
to the right.
We also know that there are several important phenomena for wave
propagating in non-uniform
media, such as: reflection, refraction, diffraction, and scattering.
My question is, for plane wave, f(x+c*t) can be understood as reflection,
but how about f(x-c*t)?
A next question is for more general wave form. Can we separately correlate
those wave phenomena
with f(x+c*t) and f(x-c*t)?
Thanks,
by Cheng Cosine
Jan/02/2k5 UT
.
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| User: "Franz Heymann" |
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| Title: Re: ? phys meaning of partial wave soln |
03 Jan 2005 02:10:12 PM |
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"Cheng Cosine" <acosine@ms13.url.com.tw> wrote in message
news:cranjk$c4c$1@vegh.ks.cc.utah.edu...
Hi:
The general soln of a linear scalar wave eqn can be expressed as
f(x+c*t)+f(x-c*t).
The phys meaning of f(x+c*t) is a wave moving to the left while
f(x-c*t) is
moving
to the right.
We also know that there are several important phenomena for wave
propagating in non-uniform
media, such as: reflection, refraction, diffraction, and scattering.
My question is, for plane wave, f(x+c*t) can be understood as
reflection,
but how about f(x-c*t)?
A next question is for more general wave form. Can we separately
correlate
those wave phenomena
with f(x+c*t) and f(x-c*t)?
Hard though I may try, both your questions are as opaque as the night
as far as I am concerned.
Here's something for a trial answer:
If f(x-c*t) represents a forward going wave of arbitrary waveform,
then f(x+c*t) is the expresion for that same waveform travelling in
the backwards direction, i.e. it is a reflected wave.
Franz
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| User: "BIFF" |
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| Title: Re: ? phys meaning of partial wave soln |
03 Jan 2005 01:29:17 AM |
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Cheng Cosinewrote:
Hi:
The general soln of a linear scalar wave eqn can be expressed as
f(x+c*t)+f(x-c*t).
The phys meaning of f(x+c*t) is a wave moving to the left while
f(x-c*t) is
moving
to the right.
We also know that there are several important phenomena for wave
propagating in non-uniform
media, such as: reflection, refraction, diffraction, and
scattering.
My question is, for plane wave, f(x+c*t) can be understood as
reflection,
but how about f(x-c*t)?
A next question is for more general wave form. Can we separately
correlate
those wave phenomena
with f(x+c*t) and f(x-c*t)?
Thanks,
by Cheng Cosine
Jan/02/2k5 UT
I DONT KNOW MAYBE U R APPLYING AN EQUATON WHERE IT DOESNT APPLY THATS
WHAT MY TEECHER ALWAYS TOLD ME IN MATH CLASS BUT I STILL THINK MY
PRUFE WUZ GOOD THAT MY DOGY WUD GROW UP TO BE BIGER THEN TEH
SUN!1!11!!
*-----------------------*
Posted at:
www.GroupSrv.com
*-----------------------*
.
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| User: "PD" |
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| Title: Re: ? phys meaning of partial wave soln |
03 Jan 2005 09:05:29 AM |
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Cheng Cosine wrote:
Hi:
The general soln of a linear scalar wave eqn can be expressed as
f(x+c*t)+f(x-c*t).
The phys meaning of f(x+c*t) is a wave moving to the left while
f(x-c*t) is
moving
to the right.
We also know that there are several important phenomena for wave
propagating in non-uniform
media, such as: reflection, refraction, diffraction, and scattering.
My question is, for plane wave, f(x+c*t) can be understood as
reflection,
but how about f(x-c*t)?
A next question is for more general wave form. Can we separately
correlate
those wave phenomena
with f(x+c*t) and f(x-c*t)?
Thanks,
by Cheng Cosine
Jan/02/2k5 UT
You are imposing constraints on the solutions that are not there, and
that were assumed just for simplicity. Just to give you an example,
which wave is associated with f(x+ct) and which with f(x-ct) simply
depends on what direction you arbitrarily said was the positive
direction in the first place. If you decided differently, the two
solutions would switch. What's more important is that there *are* two
solutions to the wave equation. Physically, what this means is that
with any source of waves, there will be likely be disturbances
traveling in *both* directions along any axis. That's a much more
important insight than what behavior to associate with which.
PD
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| User: "Cheng Cosine" |
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| Title: Re: ? phys meaning of partial wave soln |
03 Jan 2005 10:58:29 AM |
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"PD" <pdraper@yahoo.com> wrote in message
news:1104764729.577699.208120@f14g2000cwb.googlegroups.com...
You are imposing constraints on the solutions that are not there, and
that were assumed just for simplicity. Just to give you an example,
which wave is associated with f(x+ct) and which with f(x-ct) simply
depends on what direction you arbitrarily said was the positive
direction in the first place. If you decided differently, the two
solutions would switch. What's more important is that there *are* two
solutions to the wave equation. Physically, what this means is that
with any source of waves, there will be likely be disturbances
traveling in *both* directions along any axis. That's a much more
important insight than what behavior to associate with which.
Suppose we have different medias along the positive z direction. We know
that
there will be reflection, transmission, and refraction since the wave
propagation
speeds in different media are different. We also know the difference on the
wave speed
influences the relative magnitudes of the wave component of reflection,
transmission, and refraction.
In the case that the difference on the wave speeds of media 1 and media 2
are not so large, one
could neglect the reflection but considering only f(z-c*t) solution. Is that
okey? Will that include
the refraction behavior if one considers only f(z-c*t) soln?
Next, there are diffraction and scattering when the wavelength is close to
some inhomogeneous
objects in the domain. Again, if I consider only the f(z-c*t) soln, can I
still observe or estimate
the diffraction and the scattering? Or how "true" does the f(z-c*t) soln
alone describe those
wave phenomena?
Thanks,
by Cheng Cosine
Jan/03/2k5 UT
.
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| User: "PD" |
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| Title: Re: ? phys meaning of partial wave soln |
03 Jan 2005 11:24:54 AM |
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Cheng Cosine wrote:
"PD" <pdraper@yahoo.com> wrote in message
news:1104764729.577699.208120@f14g2000cwb.googlegroups.com...
You are imposing constraints on the solutions that are not there,
and
that were assumed just for simplicity. Just to give you an example,
which wave is associated with f(x+ct) and which with f(x-ct) simply
depends on what direction you arbitrarily said was the positive
direction in the first place. If you decided differently, the two
solutions would switch. What's more important is that there *are*
two
solutions to the wave equation. Physically, what this means is that
with any source of waves, there will be likely be disturbances
traveling in *both* directions along any axis. That's a much more
important insight than what behavior to associate with which.
Suppose we have different medias along the positive z direction. We
know
that
there will be reflection, transmission, and refraction since the wave
propagation
speeds in different media are different. We also know the difference
on the
wave speed
influences the relative magnitudes of the wave component of
reflection,
transmission, and refraction.
In the case that the difference on the wave speeds of media 1 and
media 2
are not so large, one
could neglect the reflection but considering only f(z-c*t) solution.
Is that
okey? Will that include
the refraction behavior if one considers only f(z-c*t) soln?
Next, there are diffraction and scattering when the wavelength is
close to
some inhomogeneous
objects in the domain. Again, if I consider only the f(z-c*t) soln,
can I
still observe or estimate
the diffraction and the scattering? Or how "true" does the f(z-c*t)
soln
alone describe those
wave phenomena?
No, in general you need to include both solutions when considering
boundary transitions.
PD
.
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