| Author |
Message |
Stan Pawlukiewicz
Guest
|
 Posted:
Tue Dec 14, 2004 2:11 am Post subject:
Re: Struggling with waveform questions. |
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Stephan M. Bernsee wrote:
| Quote: | On 2004-12-13 16:06:41 +0100, Stan Pawlukiewicz <spam@spam.mitre.org> said:
Stephan M. Bernsee wrote:
On 2004-12-13 00:52:51 +0100, "Fred Marshall"
fmarshallx@remove_the_x.acm.org> said:
***The zeroeth harmonic doesn't have phase. The first harmonic does
though.... and establishes where time=0 must be relative to the
first harmonic and, thereby, the others.
The first harmonic is the fundamental (= the zeroth overtone). It
does have a phase, as does the zeroth harmonic (DC) itself. It's just
that for DC phase is a constant because it has zero frequency...
My understanding is that frequencies below the fundamental are called
sub harmonics. I interpret the zeroth harmonic to be the fundamental.
In the sort of applications I deal with, DC doesn't propagate, so I've
never thought of it as a harmonic.
The sub-harmonics usually appear at integer fractions of the frequency
of the first harmonic, so it's not at all a contradiction, just a
regular harmonic series :-)
The first sub-harmonic would appear at half the frequency of the first
harmonic, ie. one octave below it (= 1/2 f). IMHO that would be
consistent with the "fundamental" being the first harmonic (= 1/1 f),
but *not* if it were the zeroth harmonic!
So indeed your example of subharmonics is a counterexample of what you
said.
|
Perhaps, but DC would be then be then be the infinite order subharmonic.
The issue of what a zeroth order harmonic is, remains.
| Quote: |
There's another problem: in the realm of psychoacoustics, the
"fundamental" frequency (the "pitch" of a note) might not be the first
harmonic contained in a sound. Indeed, there are cases of sounds (in
speech for example) where energy at the fundamental frequency is
completely missing, so the first overtone (= second harmonic) would be
the first constituent frequency but *not* the fundamental.
Therefore, you can't just number them as they appear but you have to
evaluate the harmonic relationship as well if you really want to label a
frequency the "fundamental"...
I agree it's all a matter of convention and definition. From the musical
POV (where I come from) I have to agree with what Richard said about the
piano string. In fact, it's the exact same model I use in my "DFT à
Pied" article at http://dspdimension.com/img/sinemixl.jpg and IMHO the
only one that *really* explains this consistently.
|
I don't really like the usage "zeroth order harmonic" but I am
intereseted in the context in which the term was coined which is a
mystery. I don't think that it refered to DC. |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 2:14 am Post subject:
Re: Struggling with waveform questions. |
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glen herrmannsfeldt wrote:
...
I want to be clear that I'm not arguing, just shooting the breeze.
| Quote: | I do agree that the first harmonic is the fundamental, but
overtones are a different question. I do know that crystal
oscillators come in overtones which are odd numbers, and that crystals
can only run at odd numbers, such that the voltage on the electrodes
is different.
|
Most crystals have two terminals. What does "such that the voltage on
the electrodes is different" entail?
| Quote: | http://www.circuitcellar.com/library/print/0298/bujanos91/11.htm
|
The information on that page states that care must be taken to ensure
that overtone crystals don't revert to their fundamental frequencies.
They are generally cut so that the third overtone is more active than
any other, so not overexciting them can work. A tank circuit to allow
operation only in the vicinity of the third overtone is most reliable.
Although AFIK, there's no cut that makes the second overtone more active
than the fundamental, second-overtone operation is also possible with a
tank.
| Quote: | Which I guess I believe indicated that harmonics are multiples of the
fundaments, while overtones for a variety of physical reasons are not
exact multiples. This is true for music as well as quartz crystals.
There is an end effect such that the node or antinode is not exactly
at the end of the tube for a vibrating air column, for example. For
a string it is probably pretty close.
|
The stiffness of strings renders them inharmonic. Winding a string
increases its mass without much affecting its stiffness, making it less
inharmonic than a solid string.
| Quote: | For a quartz crystal it might be the effect of the electrodes.
|
Another kind of end effect.
| Quote: | A third overtone crystal vibrates at approximately three times the
fundamental frequency, and is called third overtone not third harmonic.
|
That's what I wrote earlier, is it not? Overtone crystals are used at
such high frequencies that a fundamental crystal would be exceedingly
thin. A factor of 2 is rarely worth while, especially considering the
need for a tank. (I had one damn thing that persisted in jumping to the
second overtone until I broke down and used a tank. Rare, though.) Very
high Q crystals are mounted in a vacuum by a pair of wires at the
centers of evaporated-on electrodes. I even operated one of those third
overtone with a push-push arrangement. Later, a fundamental version with
a push-push tripler proved more stable.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 2:21 am Post subject:
Re: Struggling with waveform questions. |
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glen herrmannsfeldt wrote:
| Quote: |
Jerry Avins wrote:
(snip on harmonics and crystals, not necessarily in that order)
That's a weasel. It's meant to oscillate at its third overtone, about 27
MHz. On the other hand, if it's run at its fundamental and fed into a
push-push tripler, it will produce exactly 27 MHz, it's third harmonic.
I don't believe this is true for crystals, though I haven't thought
about it in a while. It will be close, but not close enough for
some people. (Especially radio users with well defined frequencies.)
|
I wasn't clear. If you run a crystal at its fundamental, you get a
frequency as good as its specs. If you then use a tripler circuit, you
get the third harmonic exactly. Third overtone crystals are ground to
produce a precise operating frequency. If you run them at their
fundamentals, the frequency will be only approximately 1/3 of that.
| Quote: | If you consider the modes of an air column in a tube, such as a
pipe organ of flute you will find that the higher modes are not exactly
integer multiples. For an air column there is an end effect due to the
finite diameter of the tube, such that the boundary condition doesn't
occur right at the physical end of the tube. For crystals, it might
be due to the effects of the plated electrodes on the crystal faces not
having the same physical properties as quartz. Probably close enough
for processor clocks, though.
|
The flare at the ends of brass instruments moves the effective end of
the tube to keep the overtones in fairly harmonic relationship.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 2:29 am Post subject:
Re: Struggling with waveform questions. |
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Stephan M. Bernsee wrote:
| Quote: | On 2004-12-13 16:35:20 +0100, Jerry Avins <jya@ieee.org> said:
Frequency is the rate at which phase changes. That's a notion pretty
much inapplicable to DC. If one says that DC has constant phase, then
all instances of DC must have the same phase. What is it? Why did you
choose that one? It isn't reasonable to claim that 0, 6, and 12VDC are
really 12VDC at phase angles of 0, 30 and 90 degrees respectively. I
think it simplifies matters to take it that DC has no phase.
Jerry
Jerry, I beg you pardon if I quote you with "Zero has some funny
properties." Changing the numbers doesn't change the concept, IMHO, so
the concept of phase doesn't go away if the frequency approaches zero.
It's the same thing when you divide by zero - you could say the result
is infinity or argue that there is no practical result from a divide by
zero.
|
Aha! You've thrown down the gauntlet! ;-p
I specify two signals of exactly the same frequency and ask if you can
measure their relative phase. What do you answer? Surely not, given your
definitions, an unqualified yes. How would you put it?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 2:31 am Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 22:11:23 +0100, Stan Pawlukiewicz <spam@spam.mitre.org> said:
| Quote: | Perhaps, but DC would be then be then be the infinite order subharmonic.
|
Yup.
| Quote: | The issue of what a zeroth order harmonic is, remains.
|
I honestly don't think there is such a thing...
We could agree on the zero order harmonic being the infinite order
subharmonic, or DC :-)
--
Stephan M. Bernsee
http://www.dspdimension.com |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 2:32 am Post subject:
Re: Struggling with waveform questions. |
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Stan Pawlukiewicz wrote:
...
| Quote: | Perhaps, but DC would be then be then be the infinite order subharmonic.
The issue of what a zeroth order harmonic is, remains.
|
...
Do you disagree that the nth harmonic has a frequency that is n times
the fundamental? Is it mostly true, with exceptions? If exceptions, what
justifies or requires them?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 2:33 am Post subject:
Re: Struggling with waveform questions. |
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Stephan M. Bernsee wrote:
| Quote: | On 2004-12-13 22:11:23 +0100, Stan Pawlukiewicz <spam@spam.mitre.org> said:
Perhaps, but DC would be then be then be the infinite order subharmonic.
Yup.
The issue of what a zeroth order harmonic is, remains.
I honestly don't think there is such a thing...
We could agree on the zero order harmonic being the infinite order
subharmonic, or DC :-)
|
Same thing, n'est pas?
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 2:57 am Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 22:29:26 +0100, Jerry Avins <jya@ieee.org> said:
| Quote: | Aha! You've thrown down the gauntlet! ;-p
I specify two signals of exactly the same frequency and ask if you can
measure their relative phase. What do you answer? Surely not, given your
definitions, an unqualified yes. How would you put it?
Jerry
|
Hmm Jerry, I think you're right: If we allow the signal to have a phase
then we can't disambiguate the amplitude which is a nasty business. If
we don't have a phase all we see is an amplitude - much nicer indeed :-)
Still I'm not sure what happens in the real world...
--
Stephan M. Bernsee
http://www.dspdimension.com |
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Randy Yates
Guest
|
| Posted:
Tue Dec 14, 2004 3:31 am Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins <jya@ieee.org> writes:
| Quote: | Randy Yates wrote:
Richard Dobson <richarddobson@blueyonder.co.uk> writes:
[...]
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
And never the twain shall communicate.
|
Was I not communicating? I stated that I understood the usage, even
though, by the definition I choose to use (which is clearly in public
usage as well), it is semantically wrong.
What some folks here seem to want to do is control the definition I
choose to use. Sorry, they don't get to do that. If such people feel
they must show their ass to me or otherwise ostracize me for my
choice, then so be it.
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr |
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glen herrmannsfeldt
Guest
|
| Posted:
Tue Dec 14, 2004 3:42 am Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
| Quote: | glen herrmannsfeldt wrote:
I want to be clear that I'm not arguing, just shooting the breeze.
|
Sounds fine to me.
| Quote: | I do agree that the first harmonic is the fundamental, but
overtones are a different question. I do know that crystal
oscillators come in overtones which are odd numbers, and that crystals
can only run at odd numbers, such that the voltage on the electrodes
is different.
Most crystals have two terminals. What does "such that the voltage on
the electrodes is different" entail?
|
That by symmetry you can't electrically excite even modes.
| Quote: | http://www.circuitcellar.com/library/print/0298/bujanos91/11.htm
The information on that page states that care must be taken to ensure
that overtone crystals don't revert to their fundamental frequencies.
They are generally cut so that the third overtone is more active than
any other, so not overexciting them can work. A tank circuit to allow
operation only in the vicinity of the third overtone is most reliable.
Although AFIK, there's no cut that makes the second overtone more active
than the fundamental, second-overtone operation is also possible with a
tank.
|
As above, I thought only odd numbers were possible, though for different
geometry things might be different.
| Quote: | Which I guess I believe indicated that harmonics are multiples of the
fundaments, while overtones for a variety of physical reasons are not
exact multiples. This is true for music as well as quartz crystals.
There is an end effect such that the node or antinode is not exactly
at the end of the tube for a vibrating air column, for example. For
a string it is probably pretty close.
The stiffness of strings renders them inharmonic. Winding a string
increases its mass without much affecting its stiffness, making it less
inharmonic than a solid string.
|
There is that, though not an end effect it does shift the frequencies.
| Quote: | For a quartz crystal it might be the effect of the electrodes.
Another kind of end effect.
A third overtone crystal vibrates at approximately three times the
fundamental frequency, and is called third overtone not third harmonic.
That's what I wrote earlier, is it not? Overtone crystals are used at
such high frequencies that a fundamental crystal would be exceedingly
thin. A factor of 2 is rarely worth while, especially considering the
need for a tank. (I had one damn thing that persisted in jumping to the
second overtone until I broke down and used a tank. Rare, though.) Very
high Q crystals are mounted in a vacuum by a pair of wires at the
centers of evaporated-on electrodes. I even operated one of those third
overtone with a push-push arrangement. Later, a fundamental version with
a push-push tripler proved more stable.
|
In the discussion there was some suggestion that overtones were numbered
differently than harmonics. It seems, though, that at least for crystal
modes they are not. Third overtone is, more or less, three times the
fundamental not four times, and is a frequency close to the third
harmonic.
I did try a simple tank on the 8284, but never convinced to to run
at 24MHz. The 22MHz crystal was cheap enough, though.
-- glen |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 3:54 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates wrote:
| Quote: | Jerry Avins <jya@ieee.org> writes:
Randy Yates wrote:
Richard Dobson <richarddobson@blueyonder.co.uk> writes:
[...]
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
And never the twain shall communicate.
Was I not communicating? I stated that I understood the usage, even
though, by the definition I choose to use (which is clearly in public
usage as well), it is semantically wrong.
What some folks here seem to want to do is control the definition I
choose to use. Sorry, they don't get to do that. If such people feel
they must show their ass to me or otherwise ostracize me for my
choice, then so be it.
|
We can communicate by clarifying the definitions we use at great length.
How much simpler to simply adopt a common definition governed by the
context! The standard definition, simple to remember and use, is that
the frequency of harmonic number n is n times the frequency of the
fundamental, and that no exceptions are necessary. Chose any other
definition you like, but remember that when communicating with others,
you may find yourself at cross purposes unless you make your private
definition explicit.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jon Harris
Guest
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| Posted:
Tue Dec 14, 2004 4:06 am Post subject:
Re: Struggling with waveform questions. |
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"Randy Yates" <yates@ieee.org> wrote in message news:acsh3k5j.fsf@ieee.org...
| Quote: | Jerry Avins <jya@ieee.org> writes:
Randy Yates wrote:
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
And never the twain shall communicate.
Was I not communicating? I stated that I understood the usage, even
though, by the definition I choose to use (which is clearly in public
usage as well), it is semantically wrong.
What some folks here seem to want to do is control the definition I
choose to use. Sorry, they don't get to do that. If such people feel
they must show their ass to me or otherwise ostracize me for my
choice, then so be it.
|
Randy, do you object to the fundamental being called the first harmonic, the
numbering of the harmonics, or both? For example, for a musical signal with a
100Hz fundamental, what do you prefer to call the 200 Hz component? The first
harmonic, the second harmonic, or something else? Just want to clarify here. |
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Jerry Avins
Guest
|
| Posted:
Tue Dec 14, 2004 4:40 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates wrote:
| Quote: | Jerry Avins <jya@ieee.org> writes:
[...] unless you make your private definition explicit.
It is NOT my private definition. As a matter of record, the usage I
advocate has been in effect for about 440 years. Yours has been around
for maybe 50 years:
http://www.etymonline.com/index.php?search=harmony&searchmode=none
It doesn't explicitly say that the fundamental is not a harmonic,
but how do you "fit together" a single entity? Answer: you don't. That
is, it is implicit that the fundamental is a separate entity from the
harmonic since the harmonic is "joined to" or "related to" the
fundamental.
|
"My" definition is in harmony with the common language of scientists,
engineers, and acousticians. When we speak of the 11th harmonic of a 100
Hz square wave, we mean 1,100 Hz. You define it to be 1,200 Hz from what
I can see. As for Pythagoras, both your usage and mine are so far
removed from his that it's easy to misinterpret his meaning when reading
his words. That's the basic problem of a vocabulary that gives common
words variant meanings.
Say it as you like. I can translate.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Richard Dobson
Guest
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| Posted:
Tue Dec 14, 2004 4:40 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates wrote:
...
| Quote: |
Here's partly where my issue with the engineering usage comes from:
the word "harmonic" obviously has a common root with the word
"harmony." In music, you have melody and harmony. The melody is not a
harmony. The harmony is separate from the melody. See, e.g.,
|
You are referring to a term that dates at least as far back as Pythagoras. When
the ancient Greeks referred to Harmony, they were not referring to our modern
notion based on chords (which was a deplorable notion to them) but in fact to
melody - the harmony of the notes of which it is composed. As indeed your cited
reference makes clear - the harmony is in the junction between two ~successive~
notes.
| Quote: | http://www.etymonline.com/index.php?search=harmony&searchmode=none
More specifically, a harmonic is a _related_ tone to the
fundamental. Thus it is set apart from the fundamental. To begin to
call the fundamental a harmonic is the beginning of obfuscation.
|
One could equally say that your attempt to redefine it is the beginning of
obfuscation! You are using the term "harmonic" where you should be using the
term "overtone", i.e. the first overtone = 2nd harmonic.
| Quote: | I believe the current engineering usage was begun many years ago by
someone who wasn't being precise.
|
The current engineering use echoes past engineering and scientific use. Why is
saying "harmonics are at multiples of the fundamental frequency" so difficult?
OK, so multiplication by 1 is an identity operation, but that does not make it
invalid. It just means we have two alternate names for one special vibrational mode.
....
| Quote: | PS: There's no such thing as a "subharmonic" either! That is another
term that's been foisted on the general public.
|
Maybe not:
A brief Google search found this, re microwave engineering:
http://www.millimeterwave.com/subharmonic.html
Or how about in the field of optics:
http://www.optics.rochester.edu:8080/users/stroud/publications/papademetriou921.html
And another, mechanical/fluid engineering:
http://www.eng-tips.com/viewthread.cfm?qid=89426&page=8
"Can a centrifugal pump induce subharmonic vibrations?
i.e. A 3000 RPM pump and motor , can vibrate at 1200 RPM ?"
"
Yes.
"
And yet another:
http://microgravity.grc.nasa.gov/fcarchive/fluids/papers/Silber/Competing_Harmonic_and.htm
and so on...
Why is an oscillation that is an integer fraction of the fundamental so
unacceptable a notion? It crops up often, in real physical systems.
Richard Dobson |
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Randy Yates
Guest
|
| Posted:
Tue Dec 14, 2004 4:40 am Post subject:
Re: Struggling with waveform questions. |
|
|
Jerry Avins <jya@ieee.org> writes:
| Quote: | [...] unless you make your private definition explicit.
|
It is NOT my private definition. As a matter of record, the usage I
advocate has been in effect for about 440 years. Yours has been around
for maybe 50 years:
http://www.etymonline.com/index.php?search=harmony&searchmode=none
It doesn't explicitly say that the fundamental is not a harmonic,
but how do you "fit together" a single entity? Answer: you don't. That
is, it is implicit that the fundamental is a separate entity from the
harmonic since the harmonic is "joined to" or "related to" the
fundamental.
--
% Randy Yates % "Bird, on the wing,
%% Fuquay-Varina, NC % goes floating by
%%% 919-577-9882 % but there's a teardrop in his eye..."
%%%% <yates@ieee.org> % 'One Summer Dream', *Face The Music*, ELO
http://home.earthlink.net/~yatescr |
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