High School Mathematics-Physics SMILE Meeting
05 March 2002
Notes Prepared by Porter Johnson
Don Kanner (Lane Tech HS Physics) -- Reed Instruments
Don showed us how to play reed instruments made from soda straws. When he shortened the straw with scissors, we heard the pitch go up, in agreement with our expectations. We would expect that the shorter the straw the higher the pitch, and the longer the straw the lower the pitch. We measured the length of the straw to be L = 0.205 m, and for the fundamental mode [with open end boundary conditions, neglecting end effects] , the wavelength should be l = 2 L = 0.41 m. The frequency can be calculated by dividing the speed v of sound (in air at 25 °C) by this wavelength; that is f = v / l = 340 m/s / 0.41 m = 830 Hz. That seemed consistent with our observations of a "shrill" sound, nearly an octave above middle A (440 Hz).
Don then sucked in some Helium gas from a balloon, and spoke a few reassuring words, sounding like Donald Duck, an erstwhile namesake. Next he took Helium into his lungs again, and blew into the straw. We expected a very high pitched sound, since the velocity of sound in Helium is about 970 m/sec, so that f = v / l = 970 m/s / 0.41 m = 2400 Hz. (This frequency could be achieved in air with a straw of length 0.07 m!) The pitch we heard with Helium was definitely higher than that obtained for the same straw with air, but by no means as high as expected. How come? One possibility was that Don was still exhaling Helium mixed with residual air in his lungs. You took our breath away, Don!
Don also gave Earl some articles and a video demonstration concerning the "dimple" in the belt mentioned by Earl in the SMILE meeting of 05 February 2002. Earl will look at them, to see if the effect is the one he mentioned, and whether the explanation is reasonable.
Walter McDonald (CPS Substitute) -- Centripetal Force
Walter constructed a conical pendulum; for details see the references http://farside.ph.utexas.edu/teaching/301/lectures/node88.html and http://www.physics.purdue.edu/demo/1D/pendulum.html. He took a piece of string about 2 meters long, and ran it through a section of a plastic drinking straw about 5 cm long. Then he tied washers of mass m on the upper end, and washers of equal mass m on the lower end. He held the plastic straw vertically and swung the upper mass m around in a circular orbit, so that the mass m on the lower end could move up and down, changing the radius of the circular orbit of the mass m on the upper end until equilibrium was reached. Equilibrium occurred at a circular radius of 0.50 meters, with the orbiting mass making 13 revolutions in 15 seconds. We calculated the velocity of the orbit to be v = 2 p r / T = 2 p (0.5 m) /(1.15 sec) = 2.73 m/sec. By setting the force m g = m v2 / r, we get v = Ö(m g r /m) = 2.23 m/sec. Very interesting, Walter!
Bill Colson (Morgan Park HS Math) -- Probability
Bill began by criticizing the order of topics in his beginning algebra textbook; Algebra I [http://www.mes-egypt.com/content/american/curriculum_outline/Math/gr8-9.doc] by Schultz, Kennedy, Ellis, and Hollewell, [Holt Rinehart Wilson 2001; ISBN 0-03-052218-8], in that "experimental probability" is introduced in Chapter 4, but "theoretical probability" is postponed until Chapter 13. Since theoretical probability is covered in the first semester syllabus and the mid-year Case Exam, it is unfortunate that this textbook was chosen for the course.
Bill then talked about the book Dueling Idiots and Other Probability Puzzlers by Paul J Nahin [Princeton U Press 2000: ISBN 0-691-00779-1]. In particular, he discussed the following problem that was appeared in the book:
In order to make subjects more likely to answer a certain Sensitive or Embarrassing Question, which should be answered "Yes" or "No", a group of 10000 subjects was given instructions to flip a coin. If the coin came up "Tails", they were to answer the Sensitive question (with a "Yes" or a "No"). If it came up "Heads", they were to flip the coin again, and answer a different question: "Did the coin show heads on the second try?" (with a "Yes" or a " No"). All answers were then put inside a box, and analyzed. The result showed 6230 "Yes" answers, and 3770 "No" answers. What were the answers to the embarrassing question?
Because there is an equal probability of Heads or Tails, about 5000 people answered the sensitive question, and 5000 answered the "second flip" question. The answers for the second flip question should be about 2500 "Yes" and 2500 "No". We subtract these from the original tabulations to learn that about 3700 answered "Yes" to the original question, versus 1270 "No". Unfortunately, there was no mention of uncertainty or accuracy of these numbers!
This is probably a very puzzling and exciting book, Bill!/
Fred Schaal (Lane Tech HS Math) -- Reports of a "bad number" in
the Magic Square/
Fred pointed out that the 9 ´ 9 Magic Square Table in the SMILE notes of 23 November 2001 contained an error. Can you find it?
"It's all my fault!" -PJ
Very keen powers of observation, Fred!
Roy Coleman (Morgan Park HS Physics) -- Various Items
Roy, we hope you get help soon!
Larry Alofs (Kenwood HS Physics) -- Glass Blocks for Optics
Larry passed out solid glass blocks [12 x 12 x 1 cm], and showed us how to do several optics experiments with them. First, we put an x-mark on a horizontal sheet of paper, stood the block up vertically on end on the paper over the x, and looked down through the top of the glass. We could see the x through the glass; in fact several images of the x were visible, because of internal reflections of the glass.
When we looked into the glass from the side, we could not see the mark. Why?
Larry passed out laser pointers, as well as 5 cm pieces of solid glass rod about 1 cm in diameter. Then we put the broad side of the glass block on a sheet of paper, traced around it, and shined the laser obliquely through a small face, using the section of glass rod to spread the beam. Then, we traced the path of the incident beam and the beam transmitted through the block onto the paper, moved the block, and then sketched in the linear path of the beam inside the block, as shown.
Larry then showed a clear plastic spiral light pipe about 1 cm in cross-section diameter and about a meter in total length, and shined a laser pointer into one end. We could see a little reflected light coming out of the sides of the light pipe, but most of the light emerged from the other end. This is a super-duper model of a fiber optic cable. Larry said that the glass blocks were expensive [$10 each], and that the laser pointers were available from Harbor Freight Tools: [http://www.harborfreight.com], but at the low price of about $10 each: [http://www.harborfreight.com/cpi/ctaf/Category.taf?CategoryID=690]. We see the point, Larry!
Bill Blunk (Joliet Central HS Physics) -- Preparation for 01
Bill pointed out that our favorite Physics Trick Day is fast approaching, and in the spirit of that occasion he showed us a small glass jam jar with the lid closed, almost filled with water [about 50 cc]. He held the jar upright and loosened its lid. To our surprise, water streamed out of the bottom of the jar. How come? There was a hole in the bottom of the jar (!), and the water remained in place until the lid was loosened. Why did that happen?
He had drilled the hole in the jar with a spear point (carbide) glass-and-tile drill [http://www.nextag.com/glass-drill-bit/search-html or http://power-tools.hardwarestore.com/54-383-drill-bits-glass-and-tile.aspx], which should be lubricated with water or kerosene during the drilling process. He had produced a very nice hole in the bottom of the glass jar -- about 3 mm [1/8"] in diameter -- which would not be evident to a casual hapless observer. Good show, Bill!
Fred Farnell (Lane Tech HS Physics) -- Dangers of Hydrogen Tankers
Fred saw a tank truck containing Liquid Hydrogen on the Dan Ryan Expressway, and raised the question of safety. This issue was discussed, and it was generally felt that Liquid Hydrogen is probably no more dangerous than such materials as Liquid Natural Gas [LNG], Kerosene, Propane, Butane, or Gasoline --- and that the most dangerous material for transport is considered to be Liquid Oxygen, according to Physics Guru and Sage Bill Shanks.
Here is an excerpt from a BBC Report on the Power of Hydrogen:
... Hydrogen can be a dangerous explosive and the thought of carrying large amounts in the tank of a car could be a bit disconcerting. But Detlef Frank believes the dangers of hydrogen are no greater than many other hazards of daily life:
‘The danger is not higher, it is different. Hydrogen is a gas that is 18 times lighter than air. So if you have a hole in your tank, for example, it just evaporates straight up. If you have a hole in a tank of, let's say, a diesel truck, you will find a little lake under your vehicle. If you are in an accident and this burns then you will be in a very bad condition. So it depends on the type of accident you have.'
See also the website of the California Hydrogen Business Council: http://www.californiahydrogen.org/, as well as of the Institute of Ecolonomics: http://www.ecolonomics.org/, founded by Dennis Weaver [remember Chester?].
Porter Johnson mentioned that hydrogen gas has a positive Joule-Kelvin
[or -Thomson, who later became Lord Kelvin]
coefficient over a
wide range of temperatures: [
The decrease in temperature which takes place when a gas expands through a throttling device as a nozzle. Also called Joule-Thomson effect. The rate of change of temperature T with pressure P in the Joule-Kelvin effect is called the Joule-Kelvin coefficientInteresting questions, Fred!
l = [ dT / dP ] hwhere h denotes constant enthalpy. For the Joule-Kelvin effect to take place the gas must initially be below its inversion temperature; if above the inversion temperature, the gas will gain heat on expansion. The inversion temperature of hydrogen, for example, is approximately -183 °C
Because we ran out of time, Ann Brandon had to postpone her presentation until next time [19 March]. See you there!
Notes taken by Porter Johnson