Does not have any harmonics

[Fleetie]

Q. "Daddy, why is the sky blue?"

In short, because air is blue.

NO.

Surely you know of Rayleigh scattering.

It doesn't require DUST in the air for the skyy to look blue. The very air molecules
themselves are sufficient.

ALSO: Wiki "water", and you'll find that pure H2O is blue-green in colour, i.e. in
its absorption spectrum. That blue-green colour arises from TWO mechanisms:

1) Optical absorption from bend/stretch/whatever in Willy Water Molecule (who is
bent!)

2) Rayleigh scattering from the molecules themselves.

Interestingly, D2O (heavy water) only exhibits effect (2) within the visible part
of the EM spectrum so should look LESS blue than H2O. That is because the
higher mass of the D atoms shifts the frequencies into the IR region.

H2O absorbs ONE HUNDRED TIMES more at the far red end of visible than at
the far blue end. Quite interesting!

Nobody knows *WHY*, other than "because that's the way it is."

Not true at all; see above and Wikipedia.


Martin

 

[Richard Henry]

simple answer.. saw and square waves are made up of hundreds of sine
waves.. sine
wave is made up of one.

Hundreds?

 

[Rich Grise]

NO.

Surely you know of Rayleigh scattering.

Yes. As I've said, that's _how_ the sky is blue, i.e., the mechanism.
("Rayleigh Scattering" is just another $.50 word for "air is blue". ;-)

But that does nothing to address _why_ it's that way.

Cheers!
Rich

 

[Rich Grise]

Hundreds?

No, it's infinity, but above some number of them their amplitudes
go below any measurable value.

Cheers!
Rich

 

[[email protected]]

Nope. Another case of "it isn't what you don't know ... but what you
think you know that ain't so".

Rayleigh scattering is proportional to the sixth power of the diameter
of the scatterer, so I automatically discounted scattering by air
molecules in favour of sub-micron dust. Thanks for the correction.

It is possible my parents didn't know better - I was four at the end
of 1946, and their university educations dated from the 1930's.
Einstein had sorted out quantitative scattering formulas in 1911, so
they could have known better, but they both majored in chemistry - and
I didn't get Rayleigh scattering in my undergraduate courses in the
1960's.

The scattering story was right - the nature of the scatterers is less
important than the fact of the scattering - and a whole lot better
than "because it is".

You are grasping at a minor flaw in the story in much the same way as
a creationist grasps at minor uncertainties in the theory of
evolution, and probably for much the same reason - you've been brought
up to believe that authority figures can give you a definitive story,
while science is all about putting together the best description that
fits the facts - Newton's Law of Graviation wasn't diminished when
Einstein extended and reinterpreted the data with general relativity.

 

[[email protected]]

Most dust is usually too large for Rayleigh scattering. Only extremely
fine nano-particles or smaller can cause wavelength dependent Rayleigh
scattering. The blue sky is seen due to scattering from the air
molecules (which are very much smaller than the wavelength of light).
It is also quite strongly polarised.

I don't recall my parents being any too specific about size of the
particles doing the scattering. They've got to be smaller than the
wavelength of visible light to do Rayleigh scattering, and liquid
water droplets that small don't last long, but there are other
candidates. Scattering strength decreases as the sixth power of the
diameter of the scatterer, so you don't need all that much sub-micron
dust to beat out 0.1 nanometer-sized molecules.

Dust and other particles larger than the wavelength of light Mie
scattering predominates (which isn't wavelength dependent). Only at
shallow angles near to the sun does Mie scattering in the atmosphere
become significantly visible. Although it can be dominant when
extremely rare and colourful stratospheric nacreous clouds are
present.

I'm happy to accept Rayleigh scattering by molecules as a sufficient
explanation for the blue of the sky. My gut feeling is that there will
often be enough sub-micron dust/ice/sulphate in the sky to make it
appreciably bluer than it would be if the air was perfectly clear.

 

[[email protected]]

In short, because air is blue.

But that's *HOW* the sky is blue.

Nobody knows *WHY*, other than "because that's the way it is."

You *are* posting as Rich the Crap Philosopher here?

In this particular case, the explanation of how the sky is blue is a
perfectly adequate explanation of why the sky is blue.

A sufficiently daft theologian might explain that God fudged the laws
of physics to make the sky blue because she liked the colour blue, but
that would just be moving the goal-posts.

 

[[email protected]]

NO.

Surely you know of Rayleigh scattering.

It doesn't require DUST in the air for the skyy to look blue. The very airmolecules
themselves are sufficient.

ALSO: Wiki "water", and you'll find that pure H2O is blue-green in colour,i.e. in
its absorption spectrum. That blue-green colour arises from TWO mechanisms:

1) Optical absorption from bend/stretch/whatever in Willy Water Molecule (who is
bent!)

The fundamental hydrogen-oxygen stretching frequencies for water are
in the near-infra red, not the visible. The bending frequencies are
all a lot lower

http://www.lsbu.ac.uk/water/vibrat.html

You do see some overtones absorption in the visible spectrum but it is
very weak.

2) Rayleigh scattering from the molecules themselves.

Interestingly, D2O (heavy water) only exhibits effect (2) within the visible part
of the EM spectrum so should look LESS blue than H2O. That is because the
higher mass of the D atoms shifts the frequencies into the IR region.

As if they weren't there to start with.

H2O absorbs ONE HUNDRED TIMES more at the far red end of visible than at
the far blue end. Quite interesting!

If you are interested in combination bands ...

 

[Rich Grise]

You *are* posting as Rich the Crap Philosopher here?

Geez, Sloman, you're nothing but a Thompson clone, but the cloning
machine reversed the polarity of your blind fanatical extremism.

Cheers!
Rich

 

[Eeyore]

Geez, Sloman, you're nothing but a Thompson clone, but the cloning
machine reversed the polarity of your blind fanatical extremism.

You pretty much hit the nail on the head there.

Graham

 

[[email protected]]

You pretty much hit the nail on the head there.

Nice to see the flakes favouring one another's nonsense.

 

[Frnak McKenney]

simple answer.. saw and square waves are made up of hundreds of sine
waves.. sine wave is made up of one.

At the risk of wandering in and appearing ignorant in two newsgroups
at once...

I think my answer to Karthik's original question would be that a
sine wave only appears "perfect" because sines (and cosines) are
(normally) the "units" of our analysis of periodic waveforms. Once
you start down that path, that is, once you say that every waveform
is "made up of" ("will be described as the combination of") some set
of scaled and shifted sine waves, then your "units" will appear to
be... um, "unitary".

But suppose some truly evil and sadistic <grin!> mathematician
decided that his classes would forever analyze periodic waveforms
using some other basis, say square waves?

Suddenly a sine wave would be seen as a truly horrible combination
of shifted and scaled square waves, a thing chock-full of
"harmonics"... it would no longer be the pristine, pure thing it
appeared when we looked at it through Fourier's eyes.

Does this make sense (even if my choice of square waves turns out to
be poor)? Or did I miss something?


--
It is a profoundly erroneous truism, repeated by all copy-books
and by eminent people when they are making speeches, that we
should cultivate the habit of thinking about what we are doing.
The precise opposite is the case. Civilization advances by
extending the numbers of important operations which we can
perform without thinking about them. Operations of thought are
like cavalry charges in battle -- they are strictly limited in
number, they require fresh horses, and must only be made at
decisive moments. -- Alfred North Whitehead

 

[Martin Brown]

At the risk of wandering in and appearing ignorant in two newsgroups
at once...

I think my answer to Karthik's original question would be that a
sine wave only appears "perfect" because sines (and cosines) are
(normally) the "units" of our analysis of periodic waveforms.  Once
you start down that path, that is, once you say that every waveform
is "made up of" ("will be described as the combination of") some set
of scaled and shifted sine waves, then your "units" will appear to
be...  um, "unitary".

It is also because of a nice property that.

d/dt cos(wt) = -wsin(wt)
and
d/dt (d/dt cos(wt) = -w^2 cos(wt)

We have Fourier to thank for this approach to periodic boundary
problems. And the sin cos functions do have some very nice proprties
like being orthogonal, complete and continuous in every derivative.

But suppose some truly evil and sadistic <grin!> mathematician
decided that his classes would forever analyze periodic waveforms
using some other basis, say square waves?

Walsh basis functions and various others that form the Hadamard matrix
can do this. In some applications they are more use than Fourier
analysis since with a bit of cunning the codec only needs add and
subtract.

Simplest being

1 1
1 -1

Then

1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1

Left as an excercise to the reader to generate the next order. These
are by construction orthogonal and complete.

http://mathworld.wolfram.com/WalshFunction.html

Suddenly a sine wave would be seen as a truly horrible combination
of shifted and scaled square waves, a thing chock-full of
"harmonics"...  it would no longer be the pristine, pure thing it
appeared when we looked at it through Fourier's eyes.

Does this make sense (even if my choice of square waves turns out to
be poor)? Or did I miss something?

If you can live with the stepwise approximation to the function then
it will work just fine. It doesn't help you solve any differential
equations though where Fourier methods are clearly superior. And the
DCT still has the edge over Hadamard the matrix for encoding images to
concentrate power in the smallest number of components.

There are lots of other decompositions of functions into orthognal
basis. Tchebechev approximation is probably the next best known and
most useful for a bounded approximation to a continuous function.
Wavelets have gained popularity for the combination of spatially
localised decompostion.

Regards,
Martin Brown

 

[Richard the Dreaded Libertarian]

You pretty much hit the nail on the head there.

Nice to see the flakes favouring one another's nonsense.[/QUOTE]

Yeah, I'm a flake. ;-) (at least _I_ _admit_ it!) The thing is,
being hated equally by both you and JT is pretty much prima facie
evidence that I'm right. ;-)

And another thing - when you crosspost, don't leave the blank
after the comma - it screws up people's newsreaders.

Cheers!
Rich

 

[[email protected]]

Yeah, I'm a flake. ;-) (at least _I_ _admit_ it!) The thing is,
being hated equally by both you and JT is pretty much prima facie
evidence that I'm right. ;-)

Hatred is a strong word. I don't think much of Jim, but I'd be
delighted if someone managed to find a treatment that arrested or
reversed his cognitive decline, not least because I've got at least
one relative who is also declining into Alzheimers.

I've even less reason to dislike you. You do enjoy saying silly
things, presumably to be provocative, since you don't seem to take
anything much seriously, but you aren't malicious.

 

[Richard the Dreaded Libertarian]

Hatred is a strong word. I don't think much of Jim, but I'd be delighted
if someone managed to find a treatment that arrested or reversed his
cognitive decline, not least because I've got at least one relative who
is also declining into Alzheimers.

Interestingly, I'd be delighted if someone managed to find a treatment
that arrested or reversed _YOUR_ cognitive decline as well, as I'm sure
Jim would. ;-) (be delighted ...)

From outside your box(es), you both appear to be victims of the same
syndrome. )-;

And you still haven't fixed your crossposter.

Good Luck!
Rich

 

[[email protected]]

Interestingly, I'd be delighted if someone managed to find a treatment
that arrested or reversed _YOUR_ cognitive decline as well, as I'm sure
Jim would. ;-) (be delighted ...)

From outside your box(es), you both appear to be victims of the same
syndrome. )-;

And you still haven't fixed your crossposter.

Good Luck!
Rich

 

[[email protected]]

Interestingly, I'd be delighted if someone managed to find a treatment
that arrested or reversed _YOUR_ cognitive decline as well, as I'm sure
Jim would. ;-) (be delighted ...)

I don't think I'm showing much sign of cognitive decline. My
psychological condition could be better - I need somewhile more
useful to do that correcting the daft ideas of the anti-global-warming
nitwits on this usergroup (of which you seem to be one) but at least
I'm aware that I've got a problem in that area. As yet there aren't
any signs of florid symptoms - like reporting people to the FBI.

From outside your box(es), you both appear to be victims of the same
syndrome. )-;

Perhaps, but at least I'm citing external evidence, rather than
relying on my inner certainies - I've still got enough insight left to
realise that what I think I know may not necessarily be so, even if it
is about something as basic as why the sky is blue.

And you still haven't fixed your crossposter.

It isn't "my" crossposter - Google groups just copies the cross-
posting line from the post I'm replying to, which is yours in this
instance, and Eeyore's when you first complained.

For the record, a newsreader that gets screwed up by spaces in a
string does no credit to the programmer who wrote the relevant bit of
code - I'd worked out how to sort out that kind of problem back in
1970 when coding in Fortran 4.

 

[John Fields]

I don't think I'm showing much sign of cognitive decline.

---
That, of course, is one of the first symptoms in that since it isn't
apparent to you, you think nothing's wrong ergo comments made by
others must be wrong.
---

My psychological condition could be better - I need somewhile more ^^^^^^^^^
something

useful to do that correcting the daft ideas of the anti-global-warming ^^^^
than

nitwits on this usergroup (of which you seem to be one) but at least
I'm aware that I've got a problem in that area. As yet there aren't
any signs of florid symptoms - like reporting people to the FBI.


Perhaps, but at least I'm citing external evidence, rather than
relying on my inner certainies

---
Except that since you're pretty set in your ways, old boy, your own
inner certainties are what drive you to believe that the external
"evidence" presented is either right or wrong, so when you read
something your inner voice tells you is wrong you reject the
"evidence" whether or whether or not it may have merit, and only
post links to "authorities" with whom you agree.

 

[Richard the Dreaded Libertarian]

Except that since you're pretty set in your ways, old boy, your own
inner certainties are what drive you to believe that the external
"evidence" presented is either right or wrong, so when you read
something your inner voice tells you is wrong you reject the "evidence"
whether or whether or not it may have merit, and only post links to

^^^^^^^^^^^^^^^^^^^^^^^^^


On the other other hand ....
;-) ;-) ;-)

"authorities" with whom you agree. ---

But apparently not about your Anthropogenic Global Warming faith, since
that's already Established Scientific Fact, right?

Feh.

"Your pulse: 98.6. Very scientific!"
"Quant Suff! Quant Suff!"

Cheers!
Rich