Phase and group velocity: a school-work experience on waves

Daniele Buongiorno, Sergej Faletič, Marisa Michelini Research Unit in Physics Education, Department of Mathematics, Informatics and Physics, University of Udine (IT)

Faculty of Mathematics and Physics, University of Ljubljana (SLO) buongiorno.daniele@spes.uniud.it, sergej.faletic@fmf.uni-lj.si, marisa.michelini@uniud.it

Piano Lauree Scientifiche IDIFO9

Università degli Studi di Udine

Introduction An educational strategy, named "school-work integration" was implemented in Italian secondary school curricula consisting a cooperation between school and employment reality that could be University. Research in physics education can contribute to the design of such educational and formative modules focusing on a specific topic [1]. In order to actively involve students in working in data collection plans for producing a significant technical and data reports, promoting at the same time an analysis of the technical characteristics of different mobile APPs allowing quantitative measurements [2] a module focused on the topic of oscillation and wave propagation was designed and carried out with 120 16-17 years old students from the Italian Scientific Lyceum L. da Vinci (Treviso, IT). Students are involved in the activity in the role of researchers to produce significant experiments with their teachers who discuss with our research group the planning of the activities supporting the students in the activities they plan on their own, without guiding or suggesting them, but simply answering to specific theoretical or technical requests. In parallel with the autonomous experimental activities, an educational path designed according to the Model of Educational Reconstruction (MER) [3] was proposed to students with the aim of clarifying the difference between phase and group velocity in the phenomena of mechanical wave propagation in a dispersive medium.

References [1] Buongiorno D., Longo A., Michelini M., Pagotto S., Ricci D., Santi L. (2019) APPs in sound measurements to gain a school-work experience, Journal of Physics Conference Series, 1223(1): 012002. [2] P. Klein, M. Hirth, S. Gröber, J. Kuhn, and A. Müller, Classical experiments revisited: Smartphone and tablet PC as experimental tools in acoustics and optics, Phys. Educ. 49 (2014) 412-418. [3] R. Duit, H. Gropengießer, U. Kattmann, M. Komorek and I. Parchmann, I., The Model of Educational Reconstruction - a framework for improving teaching and learning science, in D. Jorde & J. Dillon eds., Science

Education Research and Practice in Europe, Rotterdam, Sense Publishers (2012) 13-37.

The research is focused on the analysis of the activated operative competences after the assignments of explorative and operative tasks. Aspects regarding the role of a research-based school work in developing conceptual competences have been analyzed. A special focus has been put on students' chosen experiments for testing ideas in different ways and in employing mobile APPs. The chosen and performed experiments have been analyzed focusing on the identification of the scientific learning methodological aspects put into practice and on how those aspects are transformed into competences. In order to identify dispersion phenomena and relative peculiarities , the phenomenological study is not enough: we decided to analyze the phenomenology of superposition, in particular we focused on pulses as superposition of harmonic components, and on dispersion as a phenomenon causing the pulse shape to change while propagating.

Peculiarities of the activity

Conclusions

The Italian context: A.S.L. Law n°107/2015 “La Buona Scuola”: In order to promote working competence and students’ orienting skills, cooperation between school and employment reality is mandatory for Italian students attending the last 3 years of secondary school formation (200/400 hours): “School-Work Integration” (Alternanza Scuola-Lavoro: ASL). Public institutions, as Universities, are possible contexts. ASL is an opportunity for students to experience a real working environment supported by school, but very often this cooperation is limited to the possibility for students to: •Attend seminars •Passive employment in libraries or labs •Internships rather than formative activities

Which are more similar to teaching activities normally carried out in school; students are not asked to work on something new or to manage a project.

Dec, 7th, 2018 Jan, 31st, 2019 Feb, 23th, 2019 Mar, 18th, 2019 Mar, 29th, 2019

The external tutors (University) presented the project in plenary to students explaining the concept of mechanical/acoustic pulse by exemplifying it and involving students in simple experiments. The main APPs for the study of sound are presented and examples of use are shown. First task: Design and implement experiments that help to deepen the sources and propagation of pulses in different media; write a report on the meeting highlighting acquired concepts and encountered difficulties.

In plenary, the external tutors, after having taken up the main topics of the previous meeting, interactively and through examples introduced the concept of wave, focusing on the distinction between parameters and variables in an experiment and on the meaning of phase relation in wave propagation phenomena. The main sensors for the study of motion are then described, exemplifying their mode of use. Students are divided into 3 groups. Each group is offered a different model accounting for wave propagation: (A) dynamic model; (B) translation wave model; (C) change of reference frame.

Second task: Download the APPs, explore their sensors; produce a report on the concept of wave. Design experiments on oscillatory and periodic motions.

The groups presented the planned and implemented works. The results are discussed by making corrections and suggesting additions or changes. The external tutors involved students in simple simulations in which the sum of impulses and then waves is analyzed. The concepts of phase velocity and group velocity are explained, making use of a simulation implemented in a spreadsheet.

Third task: Using the simulation, analyze the overlap of two waves changing parameters such as amplitudes, relative phase, frequencies and velocities of propagation, producing a report on the observed outputs.

The tutors verified the understanding of the concepts of phase and group velocity also through an experience that uses a simple device made of wooden sticks; stationary waves as a particular case of overlapping waves is focused and a simulation for the Fourier analysis of a signal is presented guiding students in its use. The evidence that a pulse is the sum of infinite wave is underlined thanks to the simulation.

Fourth task: Study of the topics through experiments. Produce waves and pulses on strings/springs, make videos and see if the media is dispersive or not. Study musical signals through the APPs.

The works carried out and presented by the various groups are analyzed and corrected; further indications for improvement or completion are provided.

Fifth task: complete the experiments; individually study and write a report on the three wave models presented, highlighting advantages of each approach and aspects that are more difficult to understand.

May, 10th, 2019

Administration of a global test through «Mentimeter». Analysis of student works.

Sixth task: Complete the experiments, carry out the report and the final presentation.

Jun, 7th, 2019

Students divided in groups presented in plenary the completed works.

PULSE AS SUM OF A GREAT NUMBER

OF WAVES

Basic choice: address the contents with 16-17 y.o.students, even if waves are not scheduled in their scholastic curriculum (prerequisite: basis of kinematics and dynamics only). The theoretical framework of the MER implies a deep analysis of the founding cores and the physical aspect of the topic. In the case of wave propagation the aspects to be taken into account are the meaning of perturbation (both impulsive and periodic) propagation and the different issues tacit in different approaches to formalize the propagation itself. A study of the literature highlighted conceptual knots concerning superposition of waves: we decided to start addressing the topics in the following order: propagation of pulses, superposition of pulses, waves as a series of pulses, wave propagation, superposition of waves, change of waveform if the components have different speed, i.e. if the medium is dispersive. The activity is designed in order to allow students to have an active and interactive role: they have the responsibility of finding solutions to problems posed to them in the form of conceptual stimuli and suggest experiments. Following this approach it is possible to examine the extent to which students' responsibility activates creative and original proposals, as well as to help them to promote a critical self-evaluation stimulating the internal coherence of the proposals and the analysis, improving in this way their competences and deepening the study of the addressed concepts. The activity setting imposed: (a) different phases during a scholastic year (formative, operative, analysis and discussion) and (b) individual and cooperative tasks performed with school and University supervision .

PULSE SHAPE CHANGES WHILE PROPAGATING!