IBM Family Science Saturdays Program. IBM T.J. Watson Research Center Yorktown Heights, NY HANDOUTS

Transcription

1 IBM Family Science Saturdays Program IBM T.J. Watson Research Center Yorktown Heights, NY HANDOUTS Version Prepared by Sarunya Bangsaruntip and Katherine Saenger with input from Guy Cohen and Paul Crumley 1

2 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: Experiment 2: Discussion/Demo 3: Experiment 3: Experiment 4: Wave types and behaviors Vibrations and standing waves in Chladni plates Resonances, good and bad Singing wine glasses (glass harmonica) 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: demo) Subtractive mixing: mix your own inks (includes 3-filter Cut-out guides for glasses and bottle pitches 2

3 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. 3

4 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. 4

5 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: Stopwatch Low amplitude Motion is slow 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 amplitude) L (small amplitude) Time for 10 cycles, sec Period (time for 1 cycle), sec Frequency = 1/period, Hz Frequency/Frequency(L) L/4 (medium amplitude) High amplitude Motion is fast 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 sqrt(g/l)/(2* ) where L is the pendulum length in cm, is approximately 3.14, and g is the local gravitational acceleration (= 981 cm/sec 2 ). 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.) 5

6 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 Frequency = # of cycles per unit time Amplitude (peak-to-peak) = difference between minimum and maximum of the quantity that is varying Speed of a wave Important relationship: Speed = Frequency x Wavelength DEMO: Peak-to-peak Amplitude Low Frequency time Seeing wave with an oscilloscope! Wavelength(distance for one full cycle) Low (soft, dim) High (loud, bright) High Frequency time High Frequency Short Wavelength Low Frequency Long Wavelength 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. 6

7 Discussion/Demo 2: Wave types and behaviors, continued Types of Waves TRANSVERSE LONGITUDINAL Disturbance moves up and down, PERPENDICULAR to horizontal wave motion Example: LIGHT wave Disturbance moves back and forth sideways, in SAME DIRECTION as horizontal wave motion Example: SOUND wave Animation courtesy of Dr. Dan Russell, Kettering University 7

8 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 ( ). 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. 8

9 Discussion/Demo 3: Resonances, good and bad 9

10 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. 10

11 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 ( ) 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. 11

12 The frequencies of several musical notes are listed below. Double the frequency is an octave higher. Note Frequency (Hertz) Middle D4 E4 F4 G4 A4 B4 C5 C=C The music for Twinkle, Twinkle Little Star is written out below. 12

13 Additional resources: There is a huge amount of useful information on the Internet. Some good websites: The Tacoma Narrows Bridge video: From the University of New South Wales: Wave demos: (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 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 Color (dye) mixing: Standard inkjet refill inks from stores or internet (Cyan, Yellow, Magenta) 13

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19 Pigment Mixing (Color Subtraction) To learn more, search the web using keywords color subtraction'. Or check out this website: Magenta

20 Blue Red Magenta Black Green Color Subtraction (pigment mixing)

21 Make-your-own bottle music The six scale bars below are provided for your convenience. They are tuned for a particular plastic bottle: 4.9 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 labels from the 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 just below 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 (see backside), or play any tunes you would like! Match this line to this top rim Match this line to this bottom rim 392 Hz Hz Hz Hz 3 middle C 262 Hz Hz Hz Hz Hz Hz 3 middle C 262 Hz Hz 1 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. 392 Hz Hz Hz Hz 3 middle C 262 Hz Hz Hz Hz Hz Hz 3 middle C 262 Hz Hz Hz Hz Hz Hz 3 middle C 262 Hz Hz Hz Hz Hz Hz 3 middle C 262 Hz Hz cm Important: Print this page out at 100% size. The distance between these two lines should be 10.6 cm.

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23 Make-your-own 3-D glasses 1 Tape/glue here Right eye BLUE filter Left eye RED filter Tape/glue here 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. 2 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 3 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: (Roscolux Medium Blue 83 and E-Colour Rosco Bright Red 26).