Wavenumber?
 

On 2/16/2016 12:31 AM, Sal M. O'Nella wrote:


"gareth" wrote in message ...

Some texts give wavenumber as radians per metre, whereas others give
it as cycles per metre, for a propagating wave over a distance.

Which is preferred?

================================================== =======

My recollections for formulae is that most use radians. Lower case
omega is angular velocity in radian/sec. Divide by 2-pi for Hz, I believe.

"Sal"


I have not seen all of the earlier discussion. But: If you are going to
plug the results into trig functions (sine, tangent, etc.) or expect to
get them from inverse trig functions, the usual trig functions are more
conveniently used with radians. Any other units require "fudge factors"
like 180/Pi. So that is a reason on the radians side.
(Is that called a fiddle factor on other side of the big pond?)
Bob

Wavenumber?
 

"Bob Wilson" wrote in message
...
On 2/16/2016 12:31 AM, Sal M. O'Nella wrote:
"gareth" wrote in message ...
Some texts give wavenumber as radians per metre, whereas others give
it as cycles per metre, for a propagating wave over a distance.
Which is preferred?
================================================== =======
My recollections for formulae is that most use radians. Lower case
omega is angular velocity in radian/sec. Divide by 2-pi for Hz, I
believe.
I have not seen all of the earlier discussion. But: If you are going to
plug the results into trig functions (sine, tangent, etc.) or expect to
get them from inverse trig functions, the usual trig functions are more
conveniently used with radians. Any other units require "fudge factors"
like 180/Pi. So that is a reason on the radians side.
(Is that called a fiddle factor on other side of the big pond?)

I was digging around for the formula for a travelling wave
and encountered cos(kx-wt), where k is the wave number and
w the radians/sec, which thinking further means that k HAS to
be radians per metre and not cycles per metre.

Wavenumber?
 

In message , Jeff writes
I was digging around for the formula for a travelling wave
and encountered cos(kx-wt), where k is the wave number and
w the radians/sec, which thinking further means that k HAS to
be radians per metre and not cycles per metre.



Even a small amount of investigation will show that wave-number when
expressed in radians use the symbol k, and when expressed in
wavelength uses the symbol nu-bar 0 or a tilde above it).

Jeff



Nu (without the tiddly) is c/lambda as in E=h x nu photon energy

Damn physicists.

Brian


--
Brian Howie

Wavenumber?
 

"gareth" wrote in message ...

"Bob Wilson" wrote in message
...
On 2/16/2016 12:31 AM, Sal M. O'Nella wrote:
"gareth" wrote in message ...
Some texts give wavenumber as radians per metre, whereas others give
it as cycles per metre, for a propagating wave over a distance.
Which is preferred?
================================================== =======
My recollections for formulae is that most use radians. Lower case
omega is angular velocity in radian/sec. Divide by 2-pi for Hz, I
believe.
I have not seen all of the earlier discussion. But: If you are going to
plug the results into trig functions (sine, tangent, etc.) or expect to
get them from inverse trig functions, the usual trig functions are more
conveniently used with radians. Any other units require "fudge factors"
like 180/Pi. So that is a reason on the radians side.
(Is that called a fiddle factor on other side of the big pond?)

I was digging around for the formula for a travelling wave
and encountered cos(kx-wt), where k is the wave number and
w the radians/sec, which thinking further means that k HAS to
be radians per metre and not cycles per metre.

================================================== ===

I think we wound up this way because some people tend to think more
"comfortably" when they treat RF as a rotating vector, instead of a
recurring sine curve. I'm not one of them and omega-t has always been a
pain.

Wavenumber?
 

"Sal M. O'Nella" wrote in message
...
I think we wound up this way because some people tend to think more
"comfortably" when they treat RF as a rotating vector, instead of a
recurring sine curve. I'm not one of them and omega-t has always been a
pain.

It's another example of a little advancement in mathematics making your
whole life
easier because if you use the complex representation of cos(wt) as ..

( e^(jwt) + e^(-jwt) ) / 2

.... then it is much much easier to differentiate and
integrate exponentials than it is trig functions.

In the complex expressions above, you do, indeed, have two counter-rotating
vectors, but the simple addition of the two leaves you with a real graphical
quantity only, the
cosine that you love.

Wavenumber?
 

"gareth G4SDW GQRP #3339" wrote in message
...

"Sal M. O'Nella" wrote in message
...
I think we wound up this way because some people tend to think more
"comfortably" when they treat RF as a rotating vector, instead of a
recurring sine curve. I'm not one of them and omega-t has always been a
pain.

It's another example of a little advancement in mathematics making your
whole life
easier because if you use the complex representation of cos(wt) as ..

( e^(jwt) + e^(-jwt) ) / 2

.... then it is much much easier to differentiate and
integrate exponentials than it is trig functions.

In the complex expressions above, you do, indeed, have two counter-rotating
vectors, but the simple addition of the two leaves you with a real graphical
quantity only, the
cosine that you love.

================================================== ==========

Sure enough but I dislike the whole process of RF analysis. It stems
entirely from the fact that I'm no good at it. I struggle, I get it wrong
and I wish I had never started.

Aversion is a good teacher. Thus, I have learned, as I age, not to start
things I know I will not like.

Add "baking" to that list, if you would be so kind. :-)

"Sal"