Country: SLOVENIA (not Slovakia) Capital: LJUBLJANA Population: 2M Number of Univ.: 4 to 5.
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Transcript of 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 PlaninšičFaculty for mathematics and physics
University of Ljubljana
Slovenia
NZIP Conference 6 - 7 July 2009, Christchurch
Simple experiments and teaching
But we can do more
Excitement Inquiry
Fun Understanding
Hands-on Minds-on
Toys 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)
• 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?
These objects can emit sound
How to make it sing?Which is the best way to make it sing?
Hit with palm
Hit with rubber hammer
Blow Throw on floor
Plastic pipe
+ 0 + (best if closed at one end)
0
Al pipe 0 + + (if closed at one end)
+
Bottle 0 + + 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 COLOURPIPE LENGTH [mm]
C 328
D 290
E 258
F 243
G 216
A 193
H(B) 170
C črna 159
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
t
t
t
t
f
f f
f
BA
C D
t1 t2
t1 t2
t1 t2
t1 t2
At t1 you open the bottom end; at t2 pipe is empty
Formal thinking• Pipe closed at one end
L
cnf
L
cf
n 4
)12(40
L = 23 cm
c = 340 m/s
f0 = 370 Hz
f1 = 1110 Hz
Link theory and experiment
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?
M
RTpc
Predict – observe - explain
M
RTc
• How will the pitch of the sound emitted by the bottle change if I rinse the bottle with hot water?
2
1
2
1
T
T
f
f 1.08
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?
M
RTc
if
fi
f
i
M
M
f
f
air CO2
1.4 1.3
M 29 44Straw!
= 0.78EXP
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 modelsMeasured frequencies emitted by open pipes and pipes closed at one end are systematically lower than calculated frequencies.
L
Improved modelsMeasured frequencies emitted by open pipes and pipes closed at one end are systematically lower than calculated frequencies.
RLRLeff 61.061.0
New modelsFundamental frequency of a bottle: large discrepancy between measured and calculated values
fcalc = 405 Hz ??
fmeas = 192 Hz
Calculated
L = 21 cm
We need a better theoretical model!
Measured
L
cf
40
m
kf
2
1
L = 9cm
2r = 2 cm
V = 236 cm3
fcalc = 208 Hz
fmeas = 192 Hz
L
S = r2
V
Helmholtz resonator*
Mass (m)
Spring (k)
LV
Scf
2
Adding the neck lowers the frequency!
*T B Greenslade Jr, Experiments with Helmholtz resonators, TPT 34 (1996) 228-230
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.
L
0.224 L 0.224 L
Fundamental mode
EXP
L
0.224 L
2
2
1
2
1
L
L
Application
Wind chimes *
*D R Lapp, Building a copper pipe ‘xylophone’, Phys Educ. 38 (2003) 316-319