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Country: SLOVENIA (not Slovakia) Capital: LJUBLJANA Population: 2M Number of Univ.: 4 to 5 Multi-level simple experiments: an approach with increasing cognitive demands Gorazd Planinšič Faculty for mathematics and physics University of Ljubljana Slovenia NZIP Conference 6 - 7 July 2009, Christchurch Simple experiments and teaching Usually associated with Excitement Fun Hands-on Toys Simple experiments and teaching But we can do more Excitement Fun Understanding Hands-on Toys Inquiry Minds-on Everyday objects The aim • Sequences of structured problems intertwined with simple experiments that all together form complete stories. • The depth and cognitive level is gradually increasing from primary to university level. • Teacher may take and use just part of such a story, depending on the level she teaches. Teachers in schools need new resources • Active learning methods require more competent teacher than traditional methods. • In order to be able to prepare activities for students with different abilities, teacher needs broad repertoire of problems, tasks, themes... for each topic. Lecturers at universities can also benefit from this • Even advanced concepts and achievements of modern technology can be initially presented by means of very simple experiments. • Simple experiments can open channels for better communication between academics and students (but also between academics themselves) Singing pipes and bottles Plastic pipe d = 24 mm Al pipe d = 10mm/8mm Primary level What does these objects have in common and what are differences between them? These objects can emit sound • • • How to make them sing? Which is the best way to make a particular object sing? Are size of the object and pitch of the tone somehow related? How to make it sing? Which is the best way to make it sing? Hit with palm Hit with rubber hammer Plastic pipe + 0 Al pipe 0 + Bottle 0 + Blow + (best if Throw on floor 0 closed at one end) + (if closed at one end) + + Don’t Are size of the object and pitch of the tone related? • Shorter length => higher pitch * • It is the “empty” part of the bottle that sings * For bottles it is more tricky – we’ll come back to this at the end. EXP Make a prediction • What will you hear if I blow on a leaky bottle ? (plastic bottle half filled with water which is leaking from a hole on the bottom) Here is opportunity for connection with real life application. How? EXP Let’s play a song • Colour coded plastic pipes and... TONE COLOUR PIPE LENGTH [mm] C 328 D 290 E 258 F 243 G 216 A 193 H(B) 170 C črna 159 ... colour coded music notes. Vous Dirais-Je Maman W.A.Mozart EXP Al pipes Secondary level New concepts and “formulas” • • • • • Waves s = F(t,x) Frequency, wavelength => pitch of the tone Spectrum Reflection, superposition of waves Standing waves Technology helps • Higher frequency higher pitch • Spectrum • Standing waves in pipes Freeware Soundcard Scope: www.zeitnitz.de/Christian/Scope/Scope_en.html EXP Graphs Vertical pipe is initially closed at the bottom and half filled with water. You start blowing on the pipe to produce the sound and at t1 you open the bottom end so that water starts flowing out. At t2 the pipe is empty. Sketch a graph that will show qualitatively time dependence of fundamental frequency emitted by the pipe. Multiple choice questions At t1 you open the bottom end; at t2 pipe is empty f f t1 A t2 t1 t B t2 t t2 t f f t1 C t2 t t1 D Formal thinking • Pipe closed at one end c f0 4L ( 2n 1)c fn 4L Link theory and experiment L = 23 cm f0 = 370 Hz c = 340 m/s f1 = 1110 Hz EXP Combine several topics Pitch of the sound emitted by the pipe is directly proportional to the speed of sound. How can we change the speed of sound? What does the speed of sound depend on? c p RT M Predict – observe - explain • How will the pitch of the sound emitted by the bottle change if I rinse the bottle with hot water? RT c M f1 T1 1.08 f2 T2 EXP Predict – observe - explain • You have two equal bottles partly filled with equal amount of water. How will the pitches of the sound emitted by the bottles compare if I put an effervescent tablet into one bottle and wait until the bubbles stop forming? RT c M Straw! iM f fi = 0.78 ff f Mi EXP air CO2 1.4 1.3 M 29 44 Undergraduate university level Improved models • Hot and cold bottle: air (M=29) in the hot bottle is mixed with some water vapour (M=18) => lower effective M => higher pitch • Bottle with effervescent tablet: – Fresh air is entering the bottle due to diffusion => lower effective M => higher pitch – dissolving the tablet is endothermic reaction => lower temperature of liquid and gas => lower pitch Improved models Measured frequencies emitted by open pipes and pipes closed at one end are systematically lower than calculated frequencies. L Improved models Measured frequencies emitted by open pipes and pipes closed at one end are systematically lower than calculated frequencies. Leff 0.61 R L 0.61 R New models Fundamental frequency of a bottle: large discrepancy between measured and calculated values fmeas = 192 Hz Measured Calculated L = 21 cm f0 c 4L fcalc = 405 Hz ?? We need a better theoretical model! Helmholtz resonator* S = r 2 c1 kS ff 22 LV m L Mass (m) V Spring (k) L = 9cm Adding the neck lowers the frequency! 2r = 2 cm fcalc = 208 Hz V = 236 cm3 fmeas = 192 Hz *T B Greenslade Jr, Experiments with Helmholtz resonators, TPT 34 (1996) 228-230 Application • “Bass reflex”: improvement in low frequency response of bass loudspeakers. f Vibration of Al pipe • Sound produced by Al pipes when thrown on the floor comes mainly from transversal vibrations in metal and not from vibrations of air column. Fundamental mode L 0.224 L 0.224 L EXP Application Wind chimes * 0.224 L L 1 L1 2 L2 2 *D R Lapp, Building a copper pipe ‘xylophone’, Phys Educ. 38 (2003) 316-319 Warning All in due course of time. Don’t pour on students all the repertoire at once! Acknowledgment: Leoš Dvorak, Charles University Prague, Czech Republic Slovenian ministry for science, technology and higher education (Bilateral Project Slovenia-Czech Rep: BI-CZ/09-010-007)