IBM Family Science
IBM T.J. Watson Research Center
Yorktown Heights, NY 10598
HANDOUTS
Version 2011.1b
Prepared by Sarunya Bangsaruntip and Katherine Saenger with input
from Guy Cohen and Paul Crumley
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Waves and Resonances, Sound and Light
Introductory Notes
Experiments and Demonstrations
Discussion/demo 1:
What is an oscillation?
Experiment 1 (group):
Measuring the frequency of a pendulum
Discussion/demo 2:
Wave types and behaviors
Experiment 2:
Vibrations and standing waves in Chladni plates
Discussion/demo 3:
Resonances, good and bad
Experiment 3:
Singing wine glasses (glass harmonica)
Experiment 4:
Making music with tubes and bottles (Twinkle)
Additional Resources and notes on supplies
Discussion/demo 4:
Electromagnetic spectrum; light and color vision basics
Light wavelength/color correlation and separation
Pure colors and color mixing (additive and subtractive)
Experiment 5:
Additive mixing with finger lights (includes 2-color demo)
Experiment 6 (group):
Color filters and 3-D vision
Experiment 7:
Subtractive mixing: mix your own inks (includes 3-filter demo)
Cut-out guides for glasses and bottle pitches
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Waves and Resonances, Sound and Light
Introductory Notes
Waves and resonances, sound and light. These can be complicated topics to understand in
detail, but you already know quite a bit about them from your everyday experiences with
playground swings, musical instruments, mixing paints, and seeing color images on a computer
screen. While all of these things can be thoroughly enjoyed without any scientific explanations,
we think they can be even more fun when you know more about them.
We hope that the noisy and colorful experiments we did in this session leave you with the
enthusiasm to keep thinking about these topics, and to come up with fresh observations or
questions that you can share with your friends, ask a teacher or parent about, or research on the
Internet. We should mention that we ourselves had a lot of fun designing this class—all of us
learned things we hadn’t known before and got lots of ideas for new things to try at home.
In the pages that follow, we describe the experiments we did (quite a few of which you
may be able to repeat at home with the help of your parents). Each description lists what we
were trying to learn, the items needed to do the experiment, and what to measure. We also
include the experiment results and any miscellaneous interesting facts that we might not have
time to discuss in class.
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Experiment/demo 1: What is an oscillation?
An oscillation is a fancy word to describe a repetitive, back-and-forth motion between two
separated states. There are many examples of things that oscillate—playground swings, the
pendulum of a grandfather clock, Slinky springs, dipping/drinking bird toys, etc.
What are the characteristics of an oscillation?
PERIOD (=1/f)
• Time for one oscillation
FREQUENCY (= f)
• Number of oscillations per unit time or “rate of oscillation”
• Measured in cycles per second or Hertz
AMPLITUDE
• The magnitude (or size) of the oscillation
A low frequency oscillation has a long period.
A high frequency oscillation has a short period.
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EXPERIMENT 1 (group): How does the frequency of a pendulum depend on its length?
Intro/motivation:
The meanings of period and frequency can be easier to
remember if you have some experience in measuring these
quantities. Pendulums typically have periods and frequencies in
a range that is easy to measure quite accurately. Knowing how
the pendulum period changes with length can be useful if you
have grandfather clocks that is running too slow or too fast.
Materials:
High amplitude
Low amplitude
Motion is fast
Motion is slow
Stopwatch
Pendulum (use thread for pendulum arm; softball, fishing weight, metal nut for weight). Start
with initial pendulum length L of 1 meter.
What to do:
• Preliminary: Set pendulum in motion, watch its motion over a few cycles; practice using
the stopwatch.
• Measure time for 10 cycles of (i) long pendulum, large amplitude; (ii) long pendulum,
small amplitude, and (iii) short pendulum, medium amplitude. Fill in the table.
While doing the experiment, notice what happens to the pendulum amplitude.
L (big
L (small
L/4 (medium
amplitude)
amplitude)
amplitude)
Time for 10 cycles, sec
20
20
10
Period (time for 1 cycle), sec
2
2
1
Frequency = 1/period, Hz
0.5
0.5
1.0
Frequency/Frequency(L)
1.0
1.0
2.0
Wrap-up:
Frequency:
Longer pendulums have longer periods and lower frequency.
Effect of amplitude (wideness of swing) on frequency:
Frequency is approximately independent of amplitude: higher speed and longer distance of
high amplitude motion cancel out to keep time for one cycle the same
Friction (at pivot point and from air resistance) makes amplitude decrease in time
How is pendulum frequency affected by mass? Very little effect—something to try at home…
Historical notes, extra details:
Frequency of a pendulum in Hz is given by 2**sqrt(g/L) where L is the pendulum length in
cm, is approximately 3.14, and g is the local gravitational acceleration (= 981 cm/sec2). The
value of g can depend on where you are (it is 0.3% lower at the equator than at the poles and a
factor of 6 lower on the moon).
The pendulum frequency DOES depend on the amplitude, but the effect is very small (higher
amplitude, longer period).
The plane of a pendulum’s motion can be affected by the rotation of the earth, as can be seen
by watching a Focault pendulum. (For more info, browse the Internet on this topic.)
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Discussion/demo 2: Wave types and behaviors
Sometimes oscillatory motion can produce a wave. But what exactly is a wave? We can think
of examples—water waves, radio waves, sound waves, light waves—but sometimes they are
hard to describe.
Scientists define a wave as a disturbance that travels progressively from point to point in a
medium such as a gas, a solid, or a vacuum.
The DISTURBANCE travels but the MEDIUM (gas, solid) stays in the same place.
We demonstrated this concept with circle of kids and parents facing inward in a circle. The
people were the medium and the disturbances we tried were (i) hand-raising, and (ii) sidepushing the person to the right of you.
The characteristics of waves can be described with some of the same terms we used to
describe oscillations (frequency, amplitude) and some new ones as well (wavelength and speed).
Characteristics of Waves
Wavelength(distance for one full cycle)
Wavelength
= distance for one full cycle
Peak-to-peak
Amplitude
Frequency
= # of cycles per unit time
Amplitude (peak-to-peak)
= difference between
minimum and maximum of
the quantity that is varying
Low Frequency
Important relationship:
Speed = Frequency x Wavelength
High Frequency
High
time
Speed of a wave
DEMO:
Low
(soft, dim)
(loud, bright)
time
High Frequency
Short Wavelength
Low Frequency
Long Wavelength
Seeing wave with an oscilloscope!
Extra details:
The speed of light in a vacuum is 300 million meters (186,000 miles) per second; speed of
sound in air is about 340 meters (1/5 mile) per second. This difference in speeds can help you
judge how far away you are from a thunderstorm; you will see the lightning right away, but there
is a delay (about 5 seconds per mile) before you will hear the thunder.
The speed of a wave depends on the type of wave and the medium. The speed of sound is
faster in liquids and solids (water and steel, for example) than it is in air. In contrast, the speed of
light is slower in liquids and solids (water and glass, for example) than it is in air.
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Discussion/demo 2: Wave types and behaviors, continued
Types of Waves
TRANSVERSE
Disturbance moves up and down,
PERPENDICULAR
to horizontal wave motion
Example: LIGHT wave
LONGITUDINAL
Disturbance moves back and forth
sideways, in SAME DIRECTION as
horizontal wave motion
Example: SOUND wave
Animation courtesy of Dr. Dan Russell, Kettering University
http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html
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Experiment 2: Vibrations and Standing Waves in Chladni Plates
Motivation:
Chladni plates let you can see the beautiful patterns that can be made by vibrations and standing
waves.
Materials:
A Chladni Plate (ours was 11" x 11" x 1/8" aluminum)
Salt
Strike rod (PVC tube)
Earplugs (optional)
What to do:
Sprinkle salt on to your plate, put some earplugs in your ears (optional).
Strike the plate at the edges or corners with the PVC tube and watch what happens.
Try to make at least two different patterns.
Things to notice and think about:
Where is the plate vibrating? (Gently touch it with your finger if you can’t see it.) Where are
the nodes and the anti-nodes?
Why is the salt moving? And where is it going?
Gently touch the vibrating plate where there is salt and where there is no salt. Can you feel a
difference in vibration?
Wrap-up:
Plate vibrates with large amplitude at the strike point
Salt moves away from anti-nodes (large vibration) and settles at nodes (low vibration). So
the salt pattern is the node pattern.
A corner strike makes a cross (+); a middle edge strike makes an X.
The vibrating plate made sound waves you could hear with your ears.
Historical notes, extra details:
The Chladni plate is named after a German physicist named Ernst Chladni (1756-1827).
Chladni's first experiments were with round plates, which produced 12-pointed stars. About
his original discovery he wrote, "Just imagine my astonishment and delight upon beholding this
sight which no one had ever seen before!"
Chladni supposedly demonstrated the plates for Napoleon Bonaparte in a two-hour
audience, after which the Emperor gave Chladni 6,000 francs so that he could translate his
writings on acoustics from German into French.
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Discussion/demo 3: Resonances, good and
bad
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Experiment 3: Singing Wine Glasses
Intro/motivation:
Resonant frequencies depend on the characteristics (size,
mass, stiffness, etc.) of the part of the object is vibrating.
We perceive sounds with a high frequency as high
pitched (think of a flute or piccolo, or the right hand side of a
piano keyboard) and sounds with a low frequency as low
pitched (think of a tuba, or the left hand side of a piano
keyboard).
In our first experiment with musical acoustics we will
take a look at how the resonant frequency of a singing wine
glass depends on how much water is in it.
Materials:
Wine glass (one or more)
Water
Optional: a paper clip
What to do:
Practice making the empty wine glass sing: hold the base of the glass on a horizontal surface,
wet your finger, and CAREFULLY trace your finger over the rim. Adult supervision is
advisable. The glass will sing better if the rim is grease-free.
Add water to the glass and see if/how the pitch changes
Things to notice and think about:
Observe the water surface while the glass is singing (the effect will be more dramatic when
the glass is close to full).
Try exciting other vibration modes. You can get a sound by using a "bowing" motion across
(perpendicular to) the rim of the glass, and (if you lift up the glass and hold it by its stem) by
rubbing a wet finger around its base.
What will happen if you place a second wine glass near the one that is singing? If the second
glass is in tune with the first one, the second glass will vibrate too. A paper clip balanced on the
rim of the second glass will be a good vibration detector.
Wrap-up:
The pitch of the glass gets lower as you add water because it is
the “glass plus water” system that is vibrating.
Historical notes/extra details:
The glass harmonica is an antique musical instrument
(invented by Benjamin Franklin in 1761) whose tones are made by
singing wine glasses like the ones you experimented with. The
instrument was very popular in its day, and Mozart and Beethoven
composed music for it.
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Experiment 4: Making Musical Sounds with Bottles
Intro/motivation:
Different objects have different resonant frequencies.
A resonant chamber’s length determines the length of the
LONGEST wave that can fit in it. We demonstrated this
qualitatively by comparing the low-pitched sounds we could with a
large gallon jug to the higher-pitched sounds we could make with a
smaller 20 oz soda bottle.
Question: how can we tune a bottle resonator?
Materials:
Two or more (preferably identical) glass or plastic bottles (the scale bars at the end of the
handout are calibrated for 16.9 oz, 500 ml plastic Diet Pepsi bottles)
Water
What to do:
Practice making sounds on the bottles. Try blowing across the mouth of the bottle with the
edge of the bottle opening against and just under your bottom lip. You may have to experiment
with different “embouchure” positions to get a good sound.
Figure out how the pitch changes with the amount of water in the bottle (empty vs. filled to a
particular level mark).
If you have enough bottles (and enough people to play them) you can play a bottle music
song. “Twinkle, Twinkle, Little Star” requires 6 notes. Before playing a song, it is a good idea to
check bottle tuning by playing the notes in a scale.
Wrap-up:
Adding water to the bottle makes the pitch get higher because you are shortening the length
of the air column that is resonating.
This behavior is DIFFERENT from the behavior we saw with the wine glasses. With the
bottles, the AIR is vibrating; with the glasses the GLASS is vibrating. The resonant frequency of
an object depends on the what part of the object is vibrating.
Historical notes/details:
Bottles (and some glass Christmas tree ornaments) are examples of “Helmholtz” resonators.
Hermann von Helmholtz (1821-1894) was a German physician and physicist who did
experiments in acoustics and color vision.
Some related experiments/fun facts:
You can make your bottle “sing” by exciting it with a tuning fork matched to the bottle’s
resonance frequency. Hold the vibrating tuning fork over the mouth of the bottle, and compare
the effects for an in-tune bottle and an out-of-tune bottle.
If YOU sing at the bottle’s resonant frequency, you can sometimes feel the bottle vibrate.
The vibrating air inside the bottle makes the bottle walls vibrate.
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The frequencies of several musical notes are listed below. Double the frequency is an octave
higher.
Note
Frequency
(Hertz)
Middle
C=C4
262
D4
E4
F4
G4
A4
B4
C5
294 330
350
394
440
494 524
The music for Twinkle, Twinkle Little Star is written out below.
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Additional resources:
There is a huge amount of useful information on the Internet. Some good websites:
The Tacoma Narrows Bridge video: http://www.archive.org/details/SF121
From the University of New South Wales:
http://www.phys.unsw.edu.au/music/
http://www.phys.unsw.edu.au/primary-school-science/
Wave demos:
http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm#Slinky_Demo
http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html (Animation courtesy of
Dr. Dan Russell, Kettering University)
Wikipedia:
Suggested search terms: Chladni, Helmholtz, color theory, glass harmonica, etc.
Notes on supplies:
Color materials:
The filters used for our demonstrations were purchased from www.stagespot.com
For additive and/or 3D filters:
E-Colour Rosco Bright red 26, Roscolux Medium blue 83, and E-Colour Rosco Dark yellow
green 090 or E-color Dark green 124
For CYM color wheel (subtractive)
Roscolux Deep straw 15, Roscolux Brilliant blue 69, Roscolux Tropical Magenta 346
For RGB color wheel (subtractive)
E-Colour Rosco Light Rose 107, Roscolux Canary Yellow 312, Roscolux Jordan Blue 366
Light sources:
• Internet search on Rave finger lights, LED finger lamps, LED finger lights
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Visible light
Light is a wave
White light contains light of many different colors
Each color has its own particular wavelength
Visible light is a small part of the…
Credit: NASA via internet
1
Blue = SHORTer wavelength Red = LONGer wavelength
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Colors
Separating light
Our eyes have receptors for colors in 3 parts of the spectrum.
Colors in white light can be separated by
- prisms
- diffraction gratings
red
green
blue
R
G
B
Cool fact #1: Some “pure” (single wavelength) colors in the
spectrum can also be made by mixing.
• Yellow can be gotten straight from the spectrum
(pure color) or by mixing 2 colors of light.
Prism
Mirror
Diffraction grating
Cool Fact #2: Some colors we can see are NOT in the
light spectrum.
• Hot pink is a MIXTURE of colors.
Water
Home-made prism
DEMO:
“IBM-made” diffraction wafer
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4
Color Mixing: Subtractive & Additive
Color Mixing: Additive
Subtractive: TAKES AWAY certain wavelengths of light
Light mixing
• For light mixing to get various colors
- Inks, paints, pigments (mostly used for printing)
• Need only 3 primary colors: RGB
Red
Green
Blue
• Computer displays and
TVs create all the
colors from mixing the
3 primary colors
Additive: ADDS certain wavelengths of light
- Computer monitors, TVs, etc.
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DEMO:
Color test pattern on old TV
LCD display pixels
Additive color mixing on projectors with color filters
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Color Subtraction by Filters
Experiment Additive color mixing
white light
with finger lights!
- Compare colors with lights separated and overlapping
Interesting fact #1:
- Adjust intensities by changing distance from paper
• Red object looks red in red light.
• White object also looks red in red light.
• Therefore, red writing in white background is invisible!
Red filter
- Can you make cyan, magenta, yellow, AND white?
Red
Green
Yellow
Cyan
Interesting fact #2:
• Non-red object looks black in red light.
Red
Blue
Magenta
DEMO: Marker colors
In red light
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Color Subtraction Applications
How Depth is Perceived…
You can perceive depth because you have ….
two eyes side-by-side.
3-D Viewing
Each eye see a slightly different image!
See for yourself:
Color filtration (subtraction) can be used to trick
your brain into seeing in 3-D.
1) Hold one finger up at an arm’s length in from of you
2) Close each eye, one at a time. Do you see the exact same image?
Compare locations of your finger against a ruler below.
3) How does the shift change as you bring your finger closer/farther to your eye?
First you need to understand….
• How depth is perceived by your
eyes/brain
• How to trick your eyes/brain into
seeing depth from flat surfaces
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2
3
4
5
6
7
8
9
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When you were babies, your brain learned how to combined these
two slightly different images from each eyes into depth information
- Near-by object : Large shift in location
- Far-away object : Small shift in location
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Experiment Color filtration to select part of an image
Look at red and blue patterns below with red or blue filters (one at a time)
What do you see? What don’t you see?
http://www.casa.ucl.ac.uk/andy/blogimages/eustontowerana.jpg
BLUE RED
Seeing in 3-D: Blue and red filters are used to
let each eye see two slightly different
placements of the same object. Î Depth!!!
RIGHT
LEFT
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http://www.casa.ucl.ac.uk/andy/blogimages/eustontowerana.jpg
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Color Mixing: Subtractive (by absorption)
Printer inks
Artist paints
Yellow
Blue
Cyan
Red
Yellow
Magenta
-
With subtractive mixing, nearly all colors can be obtained
from only 3 primary colors.
Two possible sets: • Red-Blue-Yellow
• Cyan-Yellow-Magenta
DEMO:
http://apod.nasa.gov/apod/ap070602.html
2
1
1
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Color Mixing Summary
Experiment Color mixing with inks
Cyan
CMY filters
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ADDITIVE
(light mixing)
SUBTRACTIVE
(pigment mixing)
Yellow
5
2
2
1
Magenta
• Make colors using the 3 primary colors of inkjet printer inks.
• Carefully add ink droplets to water vials.
• Mix RED & BLUE
• Primary colors (3):
1 drop each
• Secondary colors (3): 2 drops each primary color
• Black:
5 drops of each primary color
– Additive
Î Magenta
– Subtractive Î Black
15
• Mix all 3 primary colors:
– Additive
Î White
– Subtractive Î Black
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2
3
Tape/glue here
1
Right eye
BLUE filter
Left eye
RED filter
Tape/glue here
Make-your-own 3-D glasses
Instructions:
1)
Tape or glue the template
provided on a heavier paper
such as card stock.
2)
Cut out the three eyeglass
parts, using the template as
a guide. Remember to cut
out the eye holes.
3)
On piece (1): Tape the red
and blue filters on to the
inside of the glasses.
(Red filter = left eye;
Blue Filter = right eye).
4)
Tape or glue the side
eyepieces (2) & (3) to (1) to
the complete your 3-D
glasses.
Note: You should have received a pair of red and blue filters from class which you can use to make your own 3-D glasses.
Should you lose them, or want more, you can find cellophane or similar materials at art and craft or party supplies stores. We
got ours from here: www.stagespot.com (Roscolux Medium Blue 83 and E-Colour Rosco Bright Red 26).
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Make-your-own bottle music
392 Hz
392 Hz
392 Hz
392 Hz
392 Hz
392 Hz
349 Hz
349 Hz
349 Hz
349 Hz
349 Hz
349 Hz
311 Hz
311 Hz
311 Hz
311 Hz
311 Hz
311 Hz
294 Hz
294 Hz
294 Hz
294 Hz
294 Hz
294 Hz
middle C
262 Hz
middle C
262 Hz
middle C
262 Hz
middle C
262 Hz
middle C
262 Hz
middle C
262 Hz
233 Hz
233 Hz
233 Hz
233 Hz
233 Hz
233 Hz
6
5
4
3
2
Match this line to
this bottom rim
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
10.6 cm
Match this line
to this top rim
Important: Print this page out at 100% size. The distance
between these two lines should be 10.6 cm.
• The six scale bars below are provided for your convenience. They are tuned for a particular plastic bottle (14.9 fl. Oz /1.05 pt/ 500 ml
Coke, either diet or regular*). This bottle has a long and skinny body, allowing for a wide range of notes.
• Remove the plastic label from each of your bottles. Cut out the scale bars along the dotted lines (as many as you need) and tape to the
bottle as shown in the diagram. Alternatively, you can trace the lines on the bottle with a marker.
• To play a particular musical note: Add water to match the water line for that note. Hold the bottle vertically, place the rim of the bottle at
your lower lip and blow gently across the top opening to produce a tone. This will take some practice, so keep trying.
• If you have six bottles, you can designate a bottle for each note. You can then re-create your own Twinkle symphony. ☺
(Music sheet can be found in an earlier page.)
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Note:• If you know a little bit about music theory, you may have noticed that this bottle scale is in the key of B flat (or A sharp).
• To learn more on how the air inside the bottle resonates, search the web for “Helmholtz resonator.”
* We don’t endorse this particular brand of beverage, by any means—this particular product just comes in a conveniently shaped bottle that can be
commonly found. Other bottles can work as well, but you will need to figure out the scale for yourself. Method 1: If you have a computer, a microphone
and an internet connection, you can use an audio processing program (such as Audacity, a free download). Method 2: Use your ears and tune the
bottles to a note on a piano or other instrument.
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