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# Re: [Phys-L] sound

• From: John Denker <jsd@av8n.com>
• Date: Sat, 13 Apr 2013 06:28:42 -0700

On 04/12/2013 10:52 AM, Anthony Lapinski wrote:

Thanks! This is very good and detailed.

:-)

Never see this in typical physics textbooks.

Yeah. Some of the books skip the topic entirely ... and other books
cover it in some detail but get the physics grotesquely wrong.

Important tangential remark: The physics of horns has many parallels
to the physics of speaking and singing.

lips <---> vocal cords

resonances <---> formants i.e. resonances
of the horn of the vocal tract

In both cases the excitation is a series of pulses, which then gets
filtered by a resonant system. Research on this dates back to the
1860s, involving some guy named Helmholtz and also some kid called
Aleck Bell.
http://en.wikipedia.org/wiki/Aleck_Bell

Not sure how can explain this in "simple" terms to my high school
students. Most of the book problems deal with the frequency equations for
strings and open/closed pipes. Given one variable (L), find the other (f),
etc. Gets more complicated when dealing with an actual instrument and what
changes to produce different notes!

Yeah, the challenge is finding ways to explain it to folks who don't
have a lot of mathematical sophistication. This applies at the HS
level and even at the college level when talking to music majors as
opposed to physics majors. My explanation in terms of convolutions
and Fourier transforms and mode locking isn't going to get a lot of
traction.

However ... there is a lot that can be done.

As for the bugle itself:
1) Start by taking the mouthpiece off and making "duck call" noises.
That is, demonstrate that you can generate any frequency you want,
over a wide range. It may take an hour or so to learn to do this if
you've never done it before, so practice in advance.

2) You are going to want a siren disk.
You can buy such a disk for a few bucks at e.g.
https://www.boreal.com/store/catalog/product.jsp?catalog_number=160046
You don't need an expensive "universal rotator"; a variable-speed
drill works just fine.

To make it more suitable for classroom demonstrations, /mark/ the disk
(in some way that doesn't block the holes) so that the rate of rotation
is easy to perceive.

This allows students to understand what a series of pulses sounds like.
You can quickly train them to associate a certain rate of rotation with
a certain sound.

3) Route the sound from the siren disk through the horn. They can see
the input and hear the output. That is to say, by watching the disk they
can infer what sound must be going into the horn, and they can hear what
comes out of the horn. If the frequency of the pulses lines up with a
resonance of the horn, a much louder sound comes out.

Vary the speed of the disk to sweep through the various resonances.

4) Explain that this model contains a crucial simplification: The horn
does not appreciably affect the disk. In a real horn, there is nonlinear
feedback. That is, the resonance of the horn affects the vibration of
the lips. HOWEVER, it remains important to take things one step at a
time. Understand how things work without this feedback before trying
to understand the feedback.

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

Also: Spectrum analyzers used to cost a king's ransom, but nowadays you
analyzer.
http://kokkinizita.linuxaudio.org/linuxaudio/pict/jaaa2.png

Set up a microphone and demonstrate a tuning fork, several simultaneous
tuning forks, a horn, a violin, a whistle, a voice singing various steady
vowels, et cetera.

This allows students to visualize what's going on in terms of frequency.
It takes some time and effort for students to figure out what the spectrum
analyzer is doing ... but this takes hours, not years. (This stands in
contrast to Fourier transforms and wavelet transforms, which HS students
are not going to understand until years later, if at all.)

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

In order to get a real understanding of what a filter is doing, it helps
to have some notion of what it means to multiply two functions point-by-
point. This is not an easy concept, but it can be explained in analogy
to adding three-dimensional vectors component-by-component. Note the
progression:
*) scalar: one number
*) vector: three components
*) a piano has 88 keys, which can be struck in any combination, which
we can write as a vector with 88 components
*) if we divide each half-step into 100 cents, that gives us 8800
different frequencies. A spectrum can be thought of as a vector
with 8800 different components. Or if you want do do it another
way, if we go from 0 to 20,000 Hz in steps of 1 Hz, that is a
vector with 20,001 components.

We can draw pictures of what it means to multiply two functions
point-by-point.

This: http://www.av8n.com/physics/img48/multiply-func-a.png
times this: http://www.av8n.com/physics/img48/multiply-func-b.png
equals this: http://www.av8n.com/physics/img48/multiply-func-ab.png

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

The following may be more appropriate for the undergraduate course than
the HS course, but let me mention it anyway:

You can buy a so-called /horn driver/ which is like a loudspeaker cone
without the cone. For less than \$30.00 including shipping, you can get
a pair of them, made by e.g. Peavy or Pyle.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&Description=horn+driver

With a little plumbing, you can attach the driver to your bugle. This
allows you to drive the horn with any signal you want. You can measure
the frequency response and the impulse response.

As mentioned in a previous note in another thread, the clever way to do
this is to play spread-spectrum pseudo-random noise with uniform energy
per unit bandwidth. You can then read off the frequency response directly.
You can also un-spread the received signal to recover the impulse response.
I have the software to do all this. If anybody is interested I can dig it
up.