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)