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From: glen herrmannsfeldt on 13 Jan 2010 12:07
Jerry Avins <jya(a)ieee.org> wrote:
(snip, I wrote)

>> Wave vector in more than one dimension. It also has the 2pi
>> that frequency doesn't normally have. (Angular frequency does.)

>> The Wave number is 2 pi/wavelength. In a dispersive
>> medium, but not too dispersive, w/k is the phase velocity,
>> dw/dk the group velocity. (w is omega, angular frequency, I don't
>> have an actual omega on this news reader.)

> Not exclusively. According to Wikipedia,
> "Wavenumber in Physics is a property of a wave defined as either

> the number of wavelengths per unit distance, that is, 1/? where
> ?=wavelength,
> or alternatively as 2?/?, sometimes termed the angular wavenumber or
> circular wavenumber or, simply wavenumber."

I only remember the one with 2pi for physics, but chemistry
might use the one without. (That is, physics done by chemists.)

I might remember a k-bar, like h-bar, as k divide by 2pi.
There is also lambda-bar, wavelength divided by 2pi.

> So without the "circular" designation, it can include 2? or not.

>> As I understand it, part of the reason was that in the early
>> days of spectroscopy c wasn't so accurately known, so reciprocal
>> wavelength was used instead. (Proportional to energy, but avoids
>> c before c was defined.)

> Right or not, that's rational, :-)

And now the meter is, more or less, defined in terms of wavelength.

-- glen

From: glen herrmannsfeldt on 13 Jan 2010 12:11
Jerry Avins <jya(a)ieee.org> wrote:
(snip)

>> This reminds me that I was recently reading about ocean (water
>> surface) waves and wave interaction. The claim is that surface
>> waves can interact (I think this would be scatter in physics
>> terminology) when the sum of the frequencies and vector sum
>> of the wave vectors is zero. That is obvioulsy true only if
>> some of the frequencies are negative. Ocean (deep water surface)
>> waves have the dispersion relation w**2=g k where k is the
>> magnitude of the wave vector, which allows for either positive
>> or negative w.

>> This reminded me of the discussion here on the meaning of
>> negative frequency. Here is an equation that only works if
>> you allow for negative frequencies!

> Words fail me! That bears deeper thought than I can do right now.

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_02.htm

-- glen
From: Jerry Avins on 13 Jan 2010 14:31
glen herrmannsfeldt wrote:
> Jerry Avins <jya(a)ieee.org> wrote:
> (snip)
>
>>> This reminds me that I was recently reading about ocean (water
>>> surface) waves and wave interaction. The claim is that surface
>>> waves can interact (I think this would be scatter in physics
>>> terminology) when the sum of the frequencies and vector sum
>>> of the wave vectors is zero. That is obvioulsy true only if
>>> some of the frequencies are negative. Ocean (deep water surface)
>>> waves have the dispersion relation w**2=g k where k is the
>>> magnitude of the wave vector, which allows for either positive
>>> or negative w.
>
>>> This reminded me of the discussion here on the meaning of
>>> negative frequency. Here is an equation that only works if
>>> you allow for negative frequencies!
>
>> Words fail me! That bears deeper thought than I can do right now.
>
> http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_02.htm

Thank you. Earlier, I had to leave for an Affordable Housing Authority
meeting. Now, I seed to give some attention to the soup on the stove.
I'll wallow in the waves later on.

Jerry
--
Engineering is the art of making what you want from things you can get.
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