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Re: [Phys-l] Harmonics vs Overtones



Hi

Roger points out an important difference between overtones and harmonics- in most real instruments overtones are not harmonic (ie. not exact multiples of the fundamental) which is why they have different timbre. In fact, because of this fact some instruments produce a perceived pitch (ie. trained musicians will match the note to a frequency generator) which is NOT a vibrational frequency of the instrument. Orchestral chimes work this way. For a given chime there is a set of overtones which are not multiples of any fundamental. Some of them, however ARE multiples of a frequency which is NOT actually present in the instrument. The ear hears these overtones and, because they are seem to be harmonics, the listener thinks they hear a fundamental frequency which is not actually there. Cheap speakers also work this way; the harmonics for a missing fundamental cause us to 'hear' a lower frequency than the speaker can actually produce.

You can set up the 'missing fundamental effect' with a couple of sine wave generators hooked up to a speaker (the sine waves should be in phase and equal amplitude). The listener adjusts a second generator/speaker combination until they think the second speaker is producing the same tone as the combined generators. Most people (including trained musicians) will pick the missing fundamental. The really interesting part is that the missing fundamental effect appears to work, even if the two 'harmonics' are fed each one, separately into each ear.

kyle

------------------------------

Message: 9
Date: Wed, 01 Apr 2009 07:00:10 -0700
From: John Denker <jsd@av8n.com>
Subject: Re: [Phys-l] Harmonics vs Overtones
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <49D3736A.8080605@av8n.com>
Content-Type: text/plain; charset=us-ascii

On 04/01/2009 06:17 AM, Tim.Odonnell@CelinaSchools.org wrote:
Would people like to elucidate on the difference between harmonics
vs overtones?

This is a terminology question, right?

I prefer to talk about _modes_. It is necessary to mention harmonics
and overtones once or twice because the terms are common in the music
business ... but the rest of the time I talk about modes.

*) One major problem with "harmonics" is that many physical systems
(including pianos) are significantly anharmonic.

*) One problem with "overtones" is that it doesn't include the
fundamental. It is needlessly complicated to talk about "fundamental
plus overtones" and much simpler to talk about modes.

Also any discussion of modes is more general, since it is not
confined to "tones". It includes optics as well as acoustics.
It includes the spatial structure of a mode, not just its time
dependence.

*) A minor (if you'll pardon the expression) problem with "modes"
is that it collides with other uses of the word "mode" in the
music business: Ionian mode, Aeolian mode, et cetera. This is
not a problem in practice; the collision is easily resolved by
context.

If that answer wasn't what was wanted, please re-ask the question.

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

On a related note (if you'll pardon the expression), it is better
to talk about a _set_ of modes rather than a "series" of modes.
In a one-dimensional tube the modes form a nice simple series,
but other systems are more complex. This includes strings (which
have two transverse polarizations) and drumheads, waveguides, atoms,
and three-dimensional resonant cavities, where it takes two or more
numbers to describe the structure of each mode.



------------------------------

Message: 10
Date: Wed, 1 Apr 2009 10:08:55 -0400
From: "Edmiston, Mike" <edmiston@bluffton.edu>
Subject: Re: [Phys-l] Harmonics vs Overtones
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Message-ID:
<D64323452018C54686455D5A09DAD9CB0BA6F83F@mail.bluffton.edu>
Content-Type: text/plain; charset="us-ascii"

The numbering system suggested is not the one I am familiar with,
neither in physics nor music.

When using "harmonics" we don't use the word fundamental. We just have
the 1st harmonic, 2nd harmonic, 3rd harmonic, etc.

When using "overtones" the lowest frequency is the fundamental, and the
1st overtone is twice the fundamental, the 2nd overtone is three-times
the fundamental, etc.

This means the equivalents are...

Fundamental = 1st harmonic

1st overtone = 2nd harmonic

2nd overtone = 3rd harmonic

Etc.

Therefore the harmonic number is one more than the overtone number
because the overtone wording begins with the fundamental, and the
harmonic wording begins with the 1st harmonic.

In usage I am familiar with, there isn't the distinction that Tim seems
to be making that the overtone series is numbered by what is heard, and
the harmonic series includes numbers for things that are not heard. The
1st overtone is twice the fundamental regardless of whether the
instrument produces the 1st overtone.

A closed organ pipe has 1st harmonic, 3rd harmonic, 5th harmonic, etc.

A closed organ pipe has fundamental, 2nd overtone, 4th overtone, etc.


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu



------------------------------

Message: 11
Date: Wed, 1 Apr 2009 10:30:33 -0400
From: Tom Sandin <sandint@ncat.edu>
Subject: Re: [Phys-l] Harmonics vs Overtones
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>,
PHYSHARE@LISTS.PSU.EDU
Cc: Tim.Odonnell@CelinaSchools.org
Message-ID: <a06240801c5f927e0e279@[152.8.29.98]>
Content-Type: text/plain; charset="us-ascii" ; format="flowed"

You are correct for the simple one-dimensional cases we talk about in
introductory courses.

I apologize to my students for the two vocabularies, but say we learn
about both because both are in common use.

The harmonic description is simplest. In our equations for allowed
wavelengths and frequencies, the integer n is the harmonic number: n
= 1 is the first harmonic, n = 2 is the second harmonic, and so on.

In the fundamental-overtone description, n = 1 gives the simplest
pattern of node(s) and antinode(s), the fundamental (lowest)
frequency, and the longest wavelength. Then the tones over that
fundamental frequency are called the overtones and so on.

I like to point out that the wavelengths and frequencies are
quantized (have certain allowed values) to lead to some simple ideas
of quantum (wave) mechanics.

Tom Sandin


At 9:17 AM -0400 4/1/09, <Tim.Odonnell@CelinaSchools.org> wrote:
Would people like to elucidate on the difference between harmonics
vs overtones?
My current thinking:
For a closed tube there can only be odd harmonics (1st - the
fundamental, 3rd, 5th, 7th, etc.), but the overtones are (1st = 3rd
harmonic, 2nd = 5th harmonic, 3rd = 7th harmonic, etc.)

For open tubes and string instruments there can be all harmonics
(1st - the fundamental, 2nd, 3rd, 4th, etc.) and for the overtones (1st
= 2nd harmonic, 2nd = 3th harmonic, 3rd = 4th harmonic, etc.)Tim
O'Donnell
Instructor of Physics and Chemistry
Celina High School
715 East Wayne Street
Celina, Ohio 45822
(419) 586-8300 Ext 1200 or 1201
odonnt@celina.k12.oh.us

"Chance only favors the prepared mind." - Louis Pasteur


_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l



------------------------------

Message: 12
Date: Wed, 1 Apr 2009 10:53:52 -0400
From: Philip Keller <PKeller@holmdelschools.org>
-----------------------------

Message: 14
Date: Wed, 01 Apr 2009 08:37:58 -0700
From: Roger Haar <haar@physics.arizona.edu>
Subject: Re: [Phys-l] Harmonics vs Overtones
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <49D38A56.9070505@physics.arizona.edu>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed

Greetings,

I think there is an important but at times subtle difference between
overtones and harmonics. On stringed instruments and organ pipes these
two ideas often overlap.

Harmonics are integer multiples of the fundamental, but for a given
system these may not be present in the sound produced.

Overtones deal with the sound actually produced. An example, given by
Wikipedia, is a drum head in which case the first overtone is 2.4 times
the fundamental. Another example is brass horns. Their overtones are
shifted a bit higher than the harmonics of the fundamental, because the
shorter wavelength sound decouples from the flare of the horn earlier in
the flare. (The pressure node of sound wave at the open end organ pipe,
is actually just beyond the end of the pipe. When the wavelength of the
sound wave becomes comparable with the diameter of the pipe or the part
of the flare things get complicated.) This shift of the overtones from
the harmonics produces the characteristic "bright" sound of a brass horn.

Sincerely,
Roger Haar






------------------------------

Message: 15
Date: Wed, 1 Apr 2009 11:43:07 -0400
From: Philip Keller <PKeller@holmdelschools.org>
Subject: Re: [Phys-l] Centrifugal redux
To: 'Forum for Physics Educators' <phys-l@carnot.physics.buffalo.edu>
Message-ID:
<6DA1C82E534FB842BBD84AE7C71734884D54A2B3CF@wrsexch3.holmdel.k12.nj.us>

Content-Type: text/plain; charset="us-ascii"



Before I talk about centrifugal forces, my students play with some Interactive Physics demonstrations: they watch what happens to a pumpkin that was riding on the roof of a car until the driver steps on the brakes. A nice feature of Interactive Physics is that you can watch the same events from different reference frames. So first we watch the pumpkin flying forward from the (apparently) stationary car, thrown forward by a "forwardial" force. Then we watch the pumpkin continue at constant velocity as the car slows down from beneath it. This time, no force acts on the pumpkin. So before my students discuss circular motion, they have already wrestled with the idea that observers in accelerating reference frames observe forces that are not observed (or needed!) by the non-accelerating observer. These discussions take up a couple of class periods but I don't see how to explain centrifugal forces to students who have not been through the linear discussion first. Then we l
ook
at what happens to a pumpkin when you go around a curve...again from both RF's.

BTW if anyone would like copies of the IP files, please email me and I'll send them over.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Marty Weiss
Sent: Wednesday, April 01, 2009 11:22 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Centrifugal redux

But, then, if you explain it in terms of *B* as you did in the
explanation for choosing *B*, well, you'd better be prepared to
elucidate that: clean up that explanation so a typical beginning
high school student would understand it and not be totally lost in
doing so. Not an easy task! (And one that may not be the best way to
approach the subject for the first time student, right or wrong.)
Look at it this way... if the student said *A* then he/she was
taught to understand it that way. They just didn't come up with that
on their own and since they are in your physics class, I would guess
that's what they got from the lessons and labs on the concept plus
from the study of Newton's Laws. If they are in physics for the first
time it's going to be rather difficult to get anyone to understand
what you mean by explanation *B* and then if you do try to correct
them you stand a good chance of losing them altogether. I can just
see the eyes glaze over and the the mind shut off with a perfunctory,
"whatever".
This is not an easy subject for most kids!

Marty


On Apr 1, 2009, at 10:53 AM, Philip Keller wrote:

Well, let me ask again (though I am tempted to let this thread go...)

Student says: A satellite remains in orbit because the
gravitational force balances the centrifugal force.

Here are some possible responses for the teacher:

A. Yes, that is correct and I have nothing more that I can add.

B. Yes, that is correct, but I would also like you to be able to
explain matters from the point of view of a non-rotating observer,
in which case you may not refer to a "centrifugal force". The
reason I want you to be able to do this is that I suspect that your
preference for the use of the rotating frame at this point in your
education masks a fundamental misunderstanding of Newton's laws.
But once you can convince me that you can do this, then please see
choice A, above.

C. No, that is incorrect because....

As a teacher, I can see that depending on who I am teaching I might
choose A, but most of the time would choose B. Can anyone finish
choice C and then tell me why I should choose it?

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu
] On Behalf Of Bill Nettles
Sent: Tuesday, March 31, 2009 10:53 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Centrifugal redux

Thanks, Joe. You said it much better than I would have. My response
was "so let's just tell them Newton's 1st law isn't that
important." Of course, we ALL have to apologize to the general
relativists because we keep talking about those fictional
gravitational forces instead of exposing them to the complex beauty
of space-time curvature and its effect on basketballs. :)

Bill

Joseph Bellina <jbellina@saintmarys.edu> 3/18/2009 11:59 am >>>
It seems to me that if you accept the student's answer you have just
lost a marvelous opportunity to reinforce the deeply counterintuitive
notion that constant velocity not at rest is the natural state of
things. Why would you waste such a gem of an opportunity to revisit
an important idea in a new framework...a key strategy in supporting
conceptual change.

cheers,

joe

Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Mar 18, 2009, at 12:53 PM, Philip Keller wrote:

I agree. If a student says that a satellite remains in orbit
because the gravitational force balances the centripetal force, I
can't say "No, you are wrong." If I insist on banishing
centrifugal forces from my class, the more honest response is: "No,
I don't want you to think about it that way." Maybe better to open
the door...time spent explaining why these forces do not really
exist could just as easily be spent explaining when it's OK to use
them.

***********

So what is the point of forcing students to go through an
intermediate
phase where they are taught centrifugal fields don't exist? For all
of their life before class, after class, and north/south/east/west of
class, centrifugal fields exist.

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


------------------------------

Message: 16
Date: Wed, 1 Apr 2009 11:46:10 -0400
From: Joseph Bellina <jbellina@saintmarys.edu>
Subject: Re: [Phys-l] Centrifugal redux
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <6DAD9FCA-5227-42A8-9269-D2EA5C222803@saintmarys.edu>
Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed

Sorry, I think that is a copout...depending on what you have done so
far, it may take several class periods to get it, but it is too
important to just say A is ok when it is not unless the student
understands rotating frames of reference, and in the context you
describe, that is highly unlikely.

It you go with A, how do you explain the earth's motion around the
sun, and still keep a coherent notion of force?

joe

Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Apr 1, 2009, at 11:22 AM, Marty Weiss wrote:

But, then, if you explain it in terms of *B* as you did in the
explanation for choosing *B*, well, you'd better be prepared to
elucidate that: clean up that explanation so a typical beginning
high school student would understand it and not be totally lost in
doing so. Not an easy task! (And one that may not be the best way to
approach the subject for the first time student, right or wrong.)
Look at it this way... if the student said *A* then he/she was
taught to understand it that way. They just didn't come up with that
on their own and since they are in your physics class, I would guess
that's what they got from the lessons and labs on the concept plus
from the study of Newton's Laws. If they are in physics for the first
time it's going to be rather difficult to get anyone to understand
what you mean by explanation *B* and then if you do try to correct
them you stand a good chance of losing them altogether. I can just
see the eyes glaze over and the the mind shut off with a perfunctory,
"whatever".
This is not an easy subject for most kids!

Marty


On Apr 1, 2009, at 10:53 AM, Philip Keller wrote:

Well, let me ask again (though I am tempted to let this thread go...)

Student says: A satellite remains in orbit because the
gravitational force balances the centrifugal force.

Here are some possible responses for the teacher:

A. Yes, that is correct and I have nothing more that I can add.

B. Yes, that is correct, but I would also like you to be able to
explain matters from the point of view of a non-rotating observer,
in which case you may not refer to a "centrifugal force". The
reason I want you to be able to do this is that I suspect that your
preference for the use of the rotating frame at this point in your
education masks a fundamental misunderstanding of Newton's laws.
But once you can convince me that you can do this, then please see
choice A, above.

C. No, that is incorrect because....

As a teacher, I can see that depending on who I am teaching I might
choose A, but most of the time would choose B. Can anyone finish
choice C and then tell me why I should choose it?

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu
] On Behalf Of Bill Nettles
Sent: Tuesday, March 31, 2009 10:53 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Centrifugal redux

Thanks, Joe. You said it much better than I would have. My response
was "so let's just tell them Newton's 1st law isn't that
important." Of course, we ALL have to apologize to the general
relativists because we keep talking about those fictional
gravitational forces instead of exposing them to the complex beauty
of space-time curvature and its effect on basketballs. :)

Bill

Joseph Bellina <jbellina@saintmarys.edu> 3/18/2009 11:59 am >>>
It seems to me that if you accept the student's answer you have just
lost a marvelous opportunity to reinforce the deeply counterintuitive
notion that constant velocity not at rest is the natural state of
things. Why would you waste such a gem of an opportunity to revisit
an important idea in a new framework...a key strategy in supporting
conceptual change.

cheers,

joe

Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Mar 18, 2009, at 12:53 PM, Philip Keller wrote:

I agree. If a student says that a satellite remains in orbit
because the gravitational force balances the centripetal force, I
can't say "No, you are wrong." If I insist on banishing
centrifugal forces from my class, the more honest response is: "No,
I don't want you to think about it that way." Maybe better to open
the door...time spent explaining why these forces do not really
exist could just as easily be spent explaining when it's OK to use
them.

***********

So what is the point of forcing students to go through an
intermediate
phase where they are taught centrifugal fields don't exist? For all
of their life before class, after class, and north/south/east/
west of
class, centrifugal fields exist.

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l



------------------------------

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


End of Phys-l Digest, Vol 51, Issue 1
*************************************

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the term "sustainable growth" is an oxymoron."
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kforinas@ius.edu
http://Physics.ius.edu/
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