2. Last year in class, students were challenged to model the motion of a molecule by randomly moving left or right for 100 steps (= N) at 1 foot per step (= L). The Einstein-Feynman prediction is that AVERAGE DISTANCE = L * √N, = 1 * √100 = 10. Click below for a simulation: http://polymer.bu.edu/java/java/1drw/ Last year in class, students were challenged to model the motion of a molecule by randomly moving left or right for 100 steps (= N) at 1 foot per step (= L). The Einstein-Feynman prediction is that AVERAGE DISTANCE = L * √N, = 1 * √100 = 10. Click below for a simulation: http://polymer.bu.edu/java/java/1drw/

3. This simulation took about 3.5 hr to run. It shows that after 5400+ trials, the average squared distance for N steps = N. So the average distance = √N, just what the Feynman formula predicts.

4. / The average distance traveled for all 50+ groups was about 9 feet. But many groups had final results that were odd numbers, ex. 1 foot, 3 feet, etc. / Is this possible? / L + R = 100. (# left steps + # right steps) So --> / L even + R even = 100. (ex. 48Lefts + 52Rights) / L odd + R odd = 100. (ex. 43Rights + 57Lefts) / But, sum of two even integers is even, and the sum of two odd integers is even, / so an odd numbered result is impossible. / The average distance traveled for all 50+ groups was about 9 feet. But many groups had final results that were odd numbers, ex. 1 foot, 3 feet, etc. / Is this possible? / L + R = 100. (# left steps + # right steps) So --> / L even + R even = 100. (ex. 48Lefts + 52Rights) / L odd + R odd = 100. (ex. 43Rights + 57Lefts) / But, sum of two even integers is even, and the sum of two odd integers is even, / so an odd numbered result is impossible.

5. / Color images require some way to generate a spectrum. How do Cathode Ray Tubes (CRTs or TVs), Liquid Crystal Displays (LCD), or plasma monitors generate millions of colors?

7. ACTIVITY 1 - Using the Mac DigitalColor Meter Application to view the RGB Channels on the Monitor 1.Open up the DigitalColor Meter on the Mac which is in Applications > Utilities folder. 2.Once you have the DigitalColor Meter opened up, paste the link below into the web browser. http://ahsastronomy.pbwiki.com/The+Spectrum. This gives us the jpg image of the spectrum below. http://ahsastronomy.pbwiki.com/The+Spectrum

8. ACTIVITY 1 con’t - Using the Mac DigitalColor Meter Application to view the RGB Channels on the Mon itor 3. Mouse over the spectrum using the DigitalColor Meter (say from red) and notice how the R, G, B values change. Relate your observations to the color wheel in the prior slide.

9. ACTIVITY 2– Using a Graphical User Interface (RGB) to produce different shades of color: Click on the following hyperlink: http://www.calculatorcat.com/ http://www.calculatorcat.com/ Click on Color Slider (RGB to hex) at the lower right side. Color Slider (RGB to hex) Two links below will work for a Windows machine. Click on http://www.softpedia.com/get/Internet/WEB-Design/Web- Design-related/RGB-Slider.shtml or http://www.blacksunsoftware.com/colormania.html to download a Windows version of a RGB Slider.) http://www.softpedia.com/get/Internet/WEB-Design/Web- Design-related/RGB-Slider.shtml http://www.blacksunsoftware.com/colormania.html

10. Activity 2 - con’t: (i) CONTINUOUS CHANGE: Move R fully to the right (other sliders left). (What do you notice?) Move G slowly to the right and note how the color changes; relate this to the spectrum. Now move R slowly to the left and relate the color change to the spectrum. Move B slowly to the right and then move G slowly left. Finally, move R slowly right, then B left. How do these changes relate to the spectrum?

11. Activity 2 - con’t: (ii) MULTIPLE SLIDERS: In turn, move each possible pair of sliders to the right keeping the other slider to the left. Predict what would happen if you slowly move the third slider to the right. Do it. What do you notice about the color?

12. (1) If Red and Green light of equal intensity are mixed, the resulting color is..... ?.. (etc.) (2) If R and G light of unequal intensity are mixed, the resulting color is. ?.. (etc.) Click on: http://en.wikipedia.org/wiki/Additive_color for more information [photo from Wikipedia ->] See the RET/2008 web page for additional activities that generate more colors.)

13. From Wikipedia, in #8 RGB phosphors are illuminated by electrons emitted from #1.

14. (1) Describe the color settings that make the color gray. Same for brown. Ditto for pink and for orange. What would you need to do to make a darker gray, brown, pink, or orange? What would you need to do to make a lighter gray, brown, pink, or orange? (2) You are interning at a theater company for the summer and will need to light a stage set and show a variety of colors, say the red-orange of a sunset or yellowish-green light from sunlight filtering through forest leaves. The Lighting Designer is about to order a complete set of 216 color filters to prepare for the show. Describe how the activities above can help you light the set without purchasing a complete set of filters.

15. Some browns. Notice the 3:2:1 intensity ratios for these shades. Suppose the ratios varied slightly from these values, what would the colors look like?

16. The full imaging lab ( see the webpage for additional content not shown above ) addresses Standard 3.1 (Unifying Themes) because students use the concept of a model and apply mathematical models to science and technology. (3.1.10.B Grade 10, p. 8) In Standard 3.4 (Physical Science, Chemistry, and Physics), students describe light effects (e.g., Doppler effect, dispersion, absorption, emission spectra, polarization, interference). (3.4.10.C Grade 10, p. 17) In Standard 3.6 (Technology Education) students apply knowledge of information technologies of encoding, transmitting, storing and retrieving and decoding.They apply and analyze advanced communication techniques to produce an image that effectively conveys a message (e.g., desktop publishing, audio, and/or video production). (3.6.10.B Grade 10, p. 23)

17. Drexel students used the Timbre Game in a lab at CAPA. Click on http://schubert.ece.drexel.edu/~raym/Ti mbreGame/TimbreGame.php http://schubert.ece.drexel.edu/~raym/Ti mbreGame/TimbreGame.php to launch the game. You will need to register in order to play it. The game is in beta version and not fully completed; clicking on Instructions does not now take you to instructions for the game.

18. The game generates musical tones showing a time graph of the amplitude and the relative strengths of the fundamental frequency and overtones. My interest is in the graph on the top.

19. The amplitude graph is similar to the graphs taught in Physical Science when students learn the basics of the physics of motion. I use an activity where students are shown various Distance vs. Time graphs and challenged to walk, or run, in a way consistent with the data the graph depicts. Distance Time This graph has the student move forward slowly, stop moving, and move backwards to the origin quickly.

20. Challenge: Students should describe how this tone sounds and then sing it. Ditto for the reverse tone?

21. Challenge: How could we describe and graph Tarzan’s jungle call? Click on http://www.geostan.ca/yells.html to get to the page shown below. The yell from his MGM days sounds like this: Tarzan at MGM.http://www.geostan.ca/yells.htmlTarzan at MGM

22. Using the graphing capability of Timbre, here’s a graph that closely approximates Tarzan’s yell.

23. The lab addresses a number of PA Academic Standards for Science and Technology, for example, for Standard 3.4 (Physical Science, Chemistry and Physics); students "describe sound effects (e.g. Doppler Effect, amplitude, frequency, reflection, refraction, absorption, sonar, seismic)." (Grade 10, p. 16) For the Academic Standards for Mathematics, the lab addresses Standard 2.5, (Mathematical Problem Solving and Communication), students will use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. (2.5.11.B, Grade 11, p. 8) For Standard 2.8 (Algebra and Functions) students will "use patterns, sequences, and series to solve routine and non-routine problems" (2.8.11C - p. 13) and they will "represent functional relationships in tables, charts and graphs." (2.8.11.Q - p. 15)