Country: SLOVENIA (not Slovakia)Capital: LJUBLJANAPopulation: 2MNumber 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

Usually associated with

Excitement

Fun

Hands-on

Toys

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)

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?

• 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

V ous D irais-J e M aman W .A .M ozar t

... colour coded music notes.

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

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

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 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

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.

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

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)