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Re: [Phys-l] harmonics




To add just a little to John's excellent comments;

For better or worse we do seem to be stuck with overtones and harmonics as terms because musicians and much of the physics literature on sound uses them, not because they are particularly good.

I have my students use the program Audacity (free!) to do spectrograms and Fourier series of their voices and instruments. It is fairly intuitive and simple to use.

An interesting example of vocal formants demonstrating the interaction of resonances and periodic excitations is the ability of 'throat singers' to sing two notes at the same time. In fact vocal formants can become part of the sound quality of some musical instruments (muliphonics).

The fact that different musicians can different Fourier spectra out of the same or identical instruments is another factor which makes it difficult to provide a single Fourier spectra for a given instrument (which was the original question I think).

kyle

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

Message: 1
Date: Sat, 19 Apr 2008 12:53:29 -0400
From: kyle forinash <kforinas@ius.edu>
Subject: Re: [Phys-l] harmonics
To: "phys-l@carnot.physics.buffalo.edu"
<phys-l@carnot.physics.buffalo.edu>
Message-ID: <480A2389.7020102@ius.edu>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed

Hi;

Take a look at these cool chladni resonances of a square plate on
YouTube: http://www.youtube.com/watch?v=Zkox6niJ1Wc

A non comprehensive, random list of odd web resources generated by
students in my sound class this semester (including the New South Wales
link mentioned below): http://physics.ius.edu/~kyle/P105/References.html

The harmonics and overtones (some of which are not harmonic) for real
instruments are incredibly complicated. Even strings and tubes are more
complicated than you might think (e.g. tubes like brass and woodwind
instruments may be conical or cylindrical along their length, not
including the bell, and have finger holes placed for the convenience of
the performer rather than optimal harmonics; stringed instruments
generally depend on body resonances of the instrument which aren't
exactly the same as the strings). Bars (marimba etc.) and drums
generally have non-harmonic overtones.

Overtones of two dimensional surfaces are also very complicated as can
be seen in the above YouTube; more so for odd shapes like piano sound
boards, guitar and violin bodies. Often the quality of the instrument
depends on the particular overtones present (e.g. wolf tones in violins)
and each individual instrument is different.

Cheers

kyle


http://physics.ius.edu/
Date: Fri, 18 Apr 2008 14:14:55 -0500 (CDT)
From: Jack Uretsky <jlu@hep.anl.gov>
Subject: Re: [Phys-l] harmonics (fwd)
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <Pine.LNX.4.64.0804181413110.16353@theory.hep.anl.gov>
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed

Hi all-
The following, courtesy of my musician office mate.
Regards,
Jack

--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley




---------- Forwarded message ----------


Hi Jack,

Harmonics in instruments depend upon many factors, even within
each instrument. A general reference for some of the timbres is
Rossing's book on "Science of Sound", 3rd Ed. He gives some general
figures for some instruments to give you an idea of their "signature".

As for the Web, the University of New South Wales in Australia has
a research institute for the physics of music and they have a wealth
of information on most instruments.

I hope that this helps.
Gordon

On 4/16/2008, "Jack Uretsky" <jlu@hep.anl.gov> wrote:

Hi Gordon-
Thought you might know the answer to this.
Regards,
Jack

--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley




---------- Forwarded message ----------

In teaching about sound, I am looking for a list of instruments and all
the harmonics they produce. I know the harmonics determine the quality of
sound from a musical instrument. Does anyone have or know of a good
website/reference/table/book that shows all the instruments, which
harmonics are present, and their relative magnitude?

_______________________________________________
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 39, Issue 24
**************************************

--
------------------------------------------
'Violence is the last refuge of the
incompetent.'
Issac Asimov

kyle forinash 812-941-2039
kforinas@ius.edu
http://Physics.ius.edu/
-----------------------------------------


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

Message: 2
Date: Sat, 19 Apr 2008 14:02:56 -0700
From: John Denker <jsd@av8n.com>
Subject: Re: [Phys-l] harmonics
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <480A5E00.7020908@av8n.com>
Content-Type: text/plain; charset=us-ascii

On 04/17/2008 09:58 AM, kyle forinash wrote:

Yes, the difference between harmonics and overtones is important.

Well, I suppose there is some importance there, but before we
take too many steps down that road, we should realize that there
is a completely different road available to us, a well-trodden
highway, simultaneously easier and more fruitful.

I recommend speaking about /resonant modes/. This is of course
related to the general idea of /resonance/ and the general idea
of /mode/. In common parlance the noun "resonance" is sometimes
used as shorthand for "resonant mode", in some contexts.

The term "resonant modes" is the physics term, It has some huge
advantages, including:
-- It treats all modes on the same footing. (This is in
contrast to the "overtone" idea, which is problematic
because the fundamental is more-or-less universally *not*
considered one of the overtones.)
-- It does not presume that the system is harmonic, or that
there is any harmonic relationship between the various
modes.
-- The same term can be used, with no change in meaning, in
electrical engineering, QM, classical physics, *and* the
physics of music.
-- It works fine for higher-dimensional systems, such as
Chladni plates and drumheads, where you need more than one
number to describe the mode (1s, 2s, 2px, 2py, et cetera)
... and you don't expect anything resembling simple integer
relationships between the resonant frequencies.
-- We can talk about the width of each resonance; we don't
need to assume the resonances have infinite Q.
-- et cetera.

I don't know of any downside to the idea (or terminology) of
resonant modes.

Many of the uses of the word "harmonic" are self-contradictory.
We do harmonic analysis to find the amount of THD (total harmonic
distortion) in a stereo system. But THD arises because the system
is anharmonic; if the system were harmonic, there wouldn't be
harmonic distortion. HOWEVER ... I can't get too excited about
this. I always start from the assumption that all terminology
is misleading. That way, if I find some terminology that isn't
toooo misleading, I'm pleasantly surprised. Don't expect the name
of a thing to tell you the nature of a thing. A titmouse is not
a kind of mouse. As Voltaire remarked, the Holy Roman Empire was
neither holy, nor Roman, nor an empire.

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

The terms "overtone" and "harmonic" are at present so entrenched
in the physics-of-music community that we have to mention them
in any course on the subject. But they can be relegated to a
subsidiary role. Resonant modes can be used as the fundamental
idea, and everything else can be defined in terms of resonant
modes. This is analogous to the way that (until recently) we
had to mention "condenser" as a deprecated synonym for capacitor
... or perhaps better, analogous to the way that imprecise
notions of "heat" become irrelevant when they are supplanted
by precise notions of energy and entropy.

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

Having said all that, there is a huge piece of physics that has
not yet been mentioned. There are quite a number of musical
instruments, including brass instruments and (!) the human
voice, where there are *two* things going on, and taking about
harmonics _or_ overtones _or_ resonances doesn't begin to paint
a correct picture of the physics.

To a useful approximation, when playing a long, constant note,
such systems can be modeled as
a) a periodic excitation, which is then acted on by
b) a set of acoustical resonant filters.

These two elements play by different rules:
a) The periodic excitation guarantees, by Floquet's theorem,
that *whatever* comes out will be periodic, with the same
period. As a corollary, we can apply Fourier methods. The
terms in the Fourier series will be related by simple integer
ratios.
a') Because the excitation is impulsive, more like a Dirac
comb than like a simple sinusoid, there will be many, many
terms in the Fourier series.
b) It is very common to find that the principal acoustical
resonances are not related in any simple way.
c) [See below.]

A lot of people get completely buffaloed by this; they have
trouble keeping both ideas (a) and (b) in their head at the
same time.

Voice is the best way I know to illustrate the relationship
between (a) and (b). On a single note (constant pitch) sing
ah eeee owe ooo. The formants (acoustical resonances) move
around, while the excitation remains essentially unchanged.
This looks good on a spectrogram. An not-very-pretty example
is:
http://static.flickr.com/91/241586415_4ff3540df8.jpg

I suppose _muting_ a horn would be another way of illustrating
the idea, but I've never actually done that experiment.

There are various software packages out there for computing
spectrograms in near-real time. I haven't evaluated them.


By the way:
c) The excitation (a) is not independent of the acoustical
resonances (b). Typically one of the acoustical resonances
(/not/ necessarily the fundamental) plays a dominant role
in setting the frequency of the excitation. In a brass
instrument, you can "lip" the excitation away from where
the acoustic resonance would naturally put it, but you
can't lip it very far.



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

Message: 3
Date: Sat, 19 Apr 2008 19:16:11 -0600
From: Larry Smith <larry.smith@snow.edu>
Subject: [Phys-l] 9.80 vs. 9.81
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Message-ID: <p06110415c43038a36d7a@[144.17.10.100]>
Content-Type: text/plain; charset="us-ascii"

The value of g at my location is less than 9.80 m/s^2, and Randy Knight
uses 9.80 in his textbook, but NIST says the accepted value for standard
gravity is 9.80665 which rounds to 9.81. Most textbooks use 9.81 when they
want three sig-figs (but not Knight).

Any thoughts?

Thanks,
Larry


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

Message: 4
Date: Sat, 19 Apr 2008 23:59:11 -0500 (CDT)
From: Jack Uretsky <jlu@hep.anl.gov>
Subject: Re: [Phys-l] 9.80 vs. 9.81
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <Pine.LNX.4.64.0804192357400.20418@theory.hep.anl.gov>
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed

How would it change your teaching of principles if you declared that g=10.
for all exercises in yor class?


On Sat, 19 Apr 2008, Larry Smith wrote:

The value of g at my location is less than 9.80 m/s^2, and Randy Knight
uses 9.80 in his textbook, but NIST says the accepted value for standard
gravity is 9.80665 which rounds to 9.81. Most textbooks use 9.81 when they
want three sig-figs (but not Knight).

Any thoughts?

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


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley





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

Message: 5
Date: Sun, 20 Apr 2008 00:07:05 -0500
From: "John Clement" <clement@hal-pc.org>
Subject: Re: [Phys-l] 9.80 vs. 9.81
To: "'Forum for Physics Educators'"
<phys-l@carnot.physics.buffalo.edu>
Message-ID: <000001c8a2a4$60758570$2201a8c0@Clement>
Content-Type: text/plain; charset="us-ascii"

This business of an accepted value is nonsense. Students are often asked to
calculate error by subtracting the accepted value from their value, when
they should be looking at how their values spread. Notice that the idea of
an accepted value makes error seem like something that is "wrong". And how
is the accepted value calculated in this case? Is it measured at a
"standard" location, or is it just an average over the entire surface of the
Earth? Or is it an average by latitude, which will give a different value.

That being said, the value that students should use is the value they
measure in the lab. Since my students do it in a very approximate fashion,
they measure 10N/kg, so that is what we use. Since the text I use also uses
this value, it is quite good enough.

One of the important reasons for using 10 is that they have previously been
told that the gravitational acceleration is 9.81, but they do not understand
this, and they are very confused when calculating F_g = m g where g is
quoted as an acceleration. After all a book on a table is not accelerating
so why use an acceleration in the calculation. But encountering the idea
that the force is 10N/kg x the mass is fairly natural. The fact that we use
a different number somewhat decouples the previous memorized knowledge from
the new understanding.

There is another problem in that g can be interpreted either as the actual
acceleration or the gravitational field constant. These yield different
values. One must make a choice there, and all too often this is glossed
over. Since my students are at a fairly low level, this distinction is
never brought out, but at all times g is treated as the gravitational field
constant.

While Knight certainly has many good things, the big misconceptions are not
always treated well. By doing Newton's laws in the numerically correct
order, they are done in the pedagogically wrong order. NTN3 needs to come
first with the idea of interactions. By deriving the local gravitational
field constant from NTN2, students are then confused. He introduces energy
bar charts, but then does not have students use them in textbook problems.
He also uses 2 types of bar charts, which can be confusing. So the research
based ideas are sometimes decorations rather than a solid part of the book.
His kinematics section is better in this regard as he does use motion maps
and graphs in textbook problems. The student workbook, however, does look
good, as it resembles McDermott tutorials.

So I would not worry about the difference between 9.80 and 9.81. This is a
small thing compared to the many other issues.

John M. Clement
Houston, TX

The value of g at my location is less than 9.80 m/s^2, and Randy Knight
uses 9.80 in his textbook, but NIST says the accepted value for standard
gravity is 9.80665 which rounds to 9.81. Most textbooks use 9.81 when
they
want three sig-figs (but not Knight).





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

Message: 6
Date: Sun, 20 Apr 2008 02:38:12 -0700
From: John Denker <jsd@av8n.com>
Subject: Re: [Phys-l] 9.80 vs. 9.81
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <480B0F04.5020404@av8n.com>
Content-Type: text/plain; charset=us-ascii

On 04/19/2008 06:16 PM, Larry Smith wrote:
The value of g at my location is less than 9.80 m/s^2, and Randy Knight
uses 9.80 in his textbook, but NIST says the accepted value for standard
gravity is 9.80665 which rounds to 9.81. Most textbooks use 9.81 when they
want three sig-figs (but not Knight).

Any thoughts?

As far as I'm concerned, the relevant rule here is:
Say what you mean, and mean what you say.

That is:
a) If you want the standard acceleration of gravity, just say so.
b) If you want the actual local acceleration of gravity at
such-and-such time and place, just say so.


A more extreme application of the same principle concerns atmospheric
pressure. The "standard atmosphere" is defined as 1 atm := 101325 Pa
exactly:
http://physics.nist.gov/Pubs/SP811/sec05.html

However, the ambient pressure in (say) Denver has never been equal to
1 atm. Not even close.
-- The difference has a significant effect on the cooking time for
hard-boiled eggs.
-- It is literally a matter of life and death when calculating aircraft
takeoff and landing performance.


Henry Kissinger said that academic fights are particularly vicious
because there is so little to fight about. Jonathan Swift also had
something to say about this.
http://www.online-literature.com/swift/gulliver/5/
AFAICT the main reason students get worked up about the distinction
between g and g_n is that for typical introductory classroom applications
it doesn't matter. (If it actually mattered, the physics would tell
you how to choose which value to use in each given situation.)



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

Message: 7
Date: Sun, 20 Apr 2008 09:24:08 -0400
From: "Michael Edmiston" <edmiston@bluffton.edu>
Subject: Re: [Phys-l] 9.80 vs. 9.81
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Message-ID: <4BCD2BEDFDE0407FADF1B21B2345EB14@MichaelEdmiston>
Content-Type: text/plain; format=flowed; charset="iso-8859-1";
reply-type=original

I would add one slight expansion to John Denker's good post on this subject.
He said "(If it actually mattered, the physics would tell you how to choose
which value to use in each given situation.)"

My comments are a little more aimed toward "good experimental practice"
telling you what value to use rather than the "physics" telling you, unless
you put good experimental practice under the umbrella of physics.

We have USGS data for several spots near our lab, including as close as a
quater mile away. We know the value is just above 9.80 and clearly rounds
to 9.80 rather than 9.81. I think it is a reasonably important lesson to
help students learn how to decide when using 9.81 is okay, or even 10, as
opposed to when they should use the known value for their location. John
alluded to this with his example of air pressure in Denver and how it be can
life and death in terms of air travel.

It may not be literal life and death to use a non-local number in your
research, although I suppose it could have an impact on the life/death of
you career, but I think students should learn to measure or research local
values for their lab work. If you are doing research in which your
calculations involve physical constants that are different in your lab from
some other lab, or from some world-wide average, why would you use the data
from some other lab or from a world-wide average? Doing so is introducing
some amount of error that is totally avoidable.

Using actual air pressure as opposed to standard pressure is one good
example that John mentioned. Likewise, the lab most likely is neither the
standard gas-law temperature of zero Celsius, nor is it the standard
temperature of 25 C used for many chemical reaction calculations, nor is it
the standard temperature of 20 C used for tabulated resistivity values or
for the calibration temperature of tuning forks.

Yes, using 9.80 rather than 9.81 for experimental calculations at my
location has little impact on the final numerical result. But that's not
the point. The point is making sure you realize you should use local values
for your research and therefore you should be in the habit of knowing how to
find these values and then using them. Early in fall semester when I tell
my physics students to see if they can find any published data for the value
of g for our location, they first seem surprised it is not 9.81. Then they
discover they don't have a clue how to go about finding it (other than
Google, which does not lead them to the USGS number for our location). At
some point, I suggest they go to the library and find the reference section
which has a lot of history and data about Bluffton, including physical data.
Surprise, they don't know where to go. Most of them know where the library
is, but they can't find the USGS data without help from the librarians.
It's a good exercise for the students, and the librarians love it because it
actually gets students into the library and asking questions. Of course,
once 25% of the class has done the work, the rest of the class doesn't need
the librarians anymore, and these procrastinators may not even go to the
library. Word spreads fast, even if I tell students not to tell other
students the number or where they found it.


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu





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

_______________________________________________
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 39, Issue 25
**************************************

--
------------------------------------------
'Violence is the last refuge of the
incompetent.'
Issac Asimov

kyle forinash 812-941-2039
kforinas@ius.edu
http://Physics.ius.edu/
-----------------------------------------