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You can see this sometimes on TV or in a movie, and it is known as the 'wagon wheel
effect' or the 'wagon wheel illusion'. This illusion can happen anytime you have two ingredients:
1) a stroboscopic (flickering) light source, illuminating or viewing 2) a
moving periodic pattern. 1) can be a movie or TV camera, a stroboscopic light, or a vibrating mirror.
2) can be the spokes in a wheel, a picket fence etc.
To show the effect, I had a bicycle wheel mounted on a wooden stand, and I borrowed a strobe light
(the black box on the right). I put bits of masking tape on the rim, since the spokes are not all that
visible. When you turn the wheel in normal light, nothing odd is visible, but of course when you turn on
the strobe, you can make the rim appear to go forward, backward, stand still etc. Check out the links
below for explanations - I don't need to repeat that. On a paper disk I drew unevenly spaced spokes.
Even when illuminated with the strobe, these never 'misbehave'. I've heard that in the old days, some
moviemakers fabricated wagon wheels with unevenly spaced spokes in order to avoid the illusion of
backward-going wheels.
Not everyone has a strobe light around the house, but if you drive the kind of car that rattles
enough to make the mirrors vibrate, look in the mirror at other car's wheels, and you can see
the wagon wheel illusion in broad daylight. [This is of course meant for the passengers - drivers
should keep their eyes on the road].
The other thing you can see in the photo is a green rubber band. If you twang hte rubber band and
adjust the strobe just right, you can make it seem as if the rubber band is vibrating very
slowly - another demonstration of the illusion.
Links:
21 January 2004
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Time to talk about nuclear fusion: 1) How atoms are put together, 2) how nuclei are put together,
3) how in a fusion reaction, a tiny bit of mass is converted to an enormous amount of energy,
via E=mc2, and 4) why it is so hard to get nuclei together (electrostatic repulsion),
and 5) how you can do it: very high temperatures.
Links about fusion:
29 January 2004
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[keep warm/cool, keep outside out, keep from drying, heat/cold/touch/pain/itch sensors,
symbiosis with
bacteria. Who has skin (endo/exo skeletons, terrestrial/aquatic), who has fur (heating/cooling). Functions of
pigmentation, vit D, general benefits of sunlight.
January 2014
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First a bit on the properties of sound: in the picture on the right is a slinky, suspended
by strings from a broom stick, and cardboard brackets which are
taped to the wall. When you tap the slinky on the end,
you can see a compression wave
travel from one side to the other (and then gets reflected).
| (In order to store this without tangling I slide everything
onto the yellow paper sleeve and tape it)
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Sound waves are compression waves:
air is easily compressible, which you can show with a (closed) soda bottle.
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| Next, I use Audacity to show soundwaves.
Nowadays, I can project on the classroom screen, record some speech, play it back,
and zoom in on the waveforms. Introduce amplitude and frequency.
The waveforms from speech and music are complicated, but if you whistle into the microphone,
you get a nearly perfect sine wave. I whistle 2 notes, one octave apart. Then we count how many
waves fit on the screen, and discover that for the higher notes, exactly twice as many waves
fit on the screen.
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I took the opportunity to do a bit of history of sound recording, starting with Thomas Edison's
cylinder phonograph of 1877, which held about 2 minute's worth of sound. Next were 78 RPM records
(very early 1900's) with about 6 minutes per side. I brought in some 78's, so the
kids could feel their weight, and because you can actually see the sound waves in the grooves with
a magnifying glass.
The player shown is from the early 1900's, when an electric motor was available, but
amplifiers were not. So the needle follows the waves in the record, and it wiggles
a tinfoil disk, producing sound. The sound travels through the tubular tone arm into the
case below, and out some holes in the front.
I played the record not only the regular way, with the steel needle in the (heavy) tonearm,
but also with just with a sheet of paper and a straightpin.
Next I play a vinyl LP, also with the
paper-and-pin. These hold 23 minutes of music per side. With a magnifying glass you can still
see the sound waves in the grooves, though they are much smaller and harder to see.
The music sounds funny, because the speed (78rpm) is higher than what it is supposed to be (33rpm)
so all frequencies are too high.
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Next: CD's developed in the 1970's. Even with a magnifying glass you really can't see what's
on there. So how does that work?
In Audacity, I zoomed in on a wave more and more. After a while, you can see that it is not
a smooth line, but just a bunch of points. Each point measures the amplitude
of the wave at that point in time. So the wave (to the computer) is just a long list of numbers, big
numbers for high amplitude, small for low amplitude. How long is this list? Normal recordings
take 40000 samples per second, so more than 2 million numbers per minute.
The numbers are converted to binary numbers, which are made up of 1's and 0's. These
are the bits and bytes in your computer. Bits are bumps on the CD surface, and the bumps are
read with the use of a laser. How small are those
bumps?
My computer tells me that an empty CD can hold 70 Mb, which is 560 000 000 bits.
The recordable area of a CD is about 85 square cm, so that each bit has to fit in an
area of 4 micrometers on a side. To set the scale, the width of a human hair is about
100 micrometers. Finally, a DVD can hold 65 times more than that (4.7 Gbytes).
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| Finally I pull up an online tone generator.
(for example, this one).
Play notes going up (recalling octaves and
frequency doubling). Going up, eventually some in the room (like me) can no longer
hear the notes. It also becomes clear that very high notes can be irritating to listen to.
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More on sound:
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Links about recording:
26 February 2004
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