|
|
| Author |
Message |
Chandru.Kundagol@gmail.co
science forum beginner
Joined: 25 Apr 2006
Posts: 2
|
 Posted: Tue Apr 25, 2006 4:36 pm Post subject:
Interpritation of the wave equation
|
|
|
Can someone briefly explain about the equation for a wave travelling
in +ve Z direction which is given as : expj(wt-beta*z).What does the
term j represent(I know it's imajinary) |
|
| Back to top |
|
 |
Timo Nieminen
science forum Guru Wannabe
Joined: 12 May 2005
Posts: 244
|
| Posted: Tue Apr 25, 2006 8:46 pm Post subject:
Re: Interpritation of the wave equation
|
|
|
On Wed, 25 Apr 2006 Chandru.Kundagol@gmail.com wrote:
| Quote: | Can someone briefly explain about the equation for a wave travelling
in +ve Z direction which is given as : expj(wt-beta*z).What does the
term j represent(I know it's imajinary)
|
Nothing. It's there for mathematical convenience, not to represent
anything. Suppose you write the electric field of an electromagnetic wave
as
E = E0 exp( ikz - iwt ).
You are _not_ saying that the above equation gives the electric field, but
that the _real part_ of the above equation gives the electric field. You
can also write
E = E0 cos( kz - wt )
with no imaginary unit in it at all. The problem is that you are also
interested in the derivatives wrt t and z, which in this case
inconveniently give you sin(..) terms. If you write exp(..), then the
derivatives are also exp(..), and you can cancel all of the exp(..) terms
in the equations, and instead of dealing with time-varying cos(..) and
sin(..) terms, you end with time-independent equations in terms of the
complex amplitudes E0 etc.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
|
| Back to top |
|
|
noshellswill
science forum beginner
Joined: 15 Apr 2006
Posts: 12
|
| Posted: Wed Apr 26, 2006 8:55 am Post subject:
Re: Interpritation of the wave equation
|
|
|
On Tue, 25 Apr 2006 09:36:08 -0700, Chandru.Kundagol wrote:
| Quote: | Can someone briefly explain about the equation for a wave travelling
in +ve Z direction which is given as : expj(wt-beta*z).What does the
term j represent(I know it's imajinary)
|
CK:
You will appreciate the "book-keeping" value of E = E0 * exp( gamma*z )
first time you solve a wave-equation. The exponential politely cancels
leaving behind useful goodies.
Try it.
nss
********* |
|
| Back to top |
|
|
John C. Polasek
science forum Guru
Joined: 30 Apr 2005
Posts: 321
|
| Posted: Thu Apr 27, 2006 6:55 pm Post subject:
Re: Interpritation of the wave equation
|
|
|
On 25 Apr 2006 09:36:08 -0700, Chandru.Kundagol@gmail.com wrote:
| Quote: | Can someone briefly explain about the equation for a wave travelling
in +ve Z direction which is given as : expj(wt-beta*z).What does the
term j represent(I know it's imajinary)
Yes it all makes good sense. Imagine an xy axis on paper with a radius |
from the intersection, rotating CCW. Then its projection on x = cos A
and on y its sin A where A is the angle from x. The machine that makes
it work is exp(jA) = E cos A + j sin A. The polar radius generates
both the x and y as it rotates through A.
You're in the complex plane and j is the vertical y axis.
Look it up a little.
John Polasek
http://www.dualspace.net |
|
| Back to top |
|
|
p.kinsler@ic.ac.uk
science forum beginner
Joined: 11 Sep 2005
Posts: 8
|
| Posted: Wed May 03, 2006 10:27 am Post subject:
Re: Interpritation of the wave equation
|
|
|
Chandru.Kundagol@gmail.com wrote:
| Quote: | Can someone briefly explain about the equation for a wave travelling
in +ve Z direction which is given as : expj(wt-beta*z).What does the
term j represent(I know it's imajinary)
|
In passing, if you want waves travelling in a particular
direction, but want to avoid those pesky exponentials,
you might be interested in
http://link.aps.org/abstract/PRA/v72/e063807
Theory of directional pulse propagation
P. Kinsler, S. B. P. Radnor, and G. H. C. New
We construct combined electric and magnetic field variables which
independently represent energy flows in the forward and backward directions,
respectively, and use these to reformulate Maxwell's equations. These
variables enable us to not only judge the effect and significance of
backward-traveling field components, but also to discard them when
appropriate. They thereby have the potential to simplify numerical
simulations, leading to potential speed gains of up to 100% over standard
finite difference time-domain (FDTD) or pseudospectral spatial-domain (PSSD)
simulations. We present results for various illustrative situations, including
an example application to second harmonic generation in periodically poled
lithium niobate. These field variables are also used to derive both envelope
equations useful for narrow-band pulse propagation, and a second order wave
equation. Alternative definitions are also presented.
--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/ |
|
| Back to top |
|
|
Google
|
|
| Back to top |
|
|
|
|
The time now is Wed Jan 07, 2009 11:50 pm | All times are GMT
|
|
Secured Loans | Myspace Graphics | Golden Sun Mp3 | Bankruptcy | Loans
|
|
Copyright © 2004-2005 DeniX Solutions SRL
|
|
Other DeniX Solutions sites:
Electronics forum |
Medicine forum |
Unix/Linux blog |
Unix/Linux documentation |
Unix/Linux forums
|
Powered by phpBB © 2001, 2005 phpBB Group
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
Forum index
»
Science and Technology
»
Physics
»
Electromagnetics
