Ivan Guastella

Modelling Mechanical Wave Propagation: Guidelines and experimentation of a teaching–learning sequence

The present paper reports the design process and the experimentation of a teaching–learning sequence about the concept of mechanical wave propagation and the role played by media where waves are propagating. The sequence focuses on the central issue of the relationships between observable phenomena, like macroscopic behaviours of waves, and their interpretation and/or explanation in terms of corpuscular characteristics of media. We describe the design process with respect to the general framework of the Educational Reconstruction Model and the pedagogical tools used. Results of a teaching/learning experiment, involving a sample of 75 high school students, are also reported. Data analysis is mainly based on qualitative research methods. The main focus is on students’ representations of phenomena and on the cognitive strategies put in action in order to modify or support their descriptive and interpretative mental models. Results are discussed by pointing out the efficacy of strategies focusing on the process of constructing predictive conceptual models and by identifying the concept of ‘level of analysis’ as different ways to look at the same phenomenon.

An experiment on the velocity distribution of thermionic electrons

This paper describes an undergraduate experiment that yields the velocity distribution of thermionic electrons by analyzing the I-V characteristics of diodes and triodes. The experiment allows students to focus on the distribution function more than on difficulties arising from the complexity of thermionic emission. By using a simple model, the velocity distribution of thermionic electrons emitted by the vacuum tube cathode can be described by Maxwell’s distribution.

A stochastic approach to quantum statistics distributions: theoretical derivation and Monte Carlo modelling

We present a method aimed at a stochastic derivation of the equilibrium distribution of a classical/quantum ideal gas in the framework of the canonical ensemble. The time evolution of these ideal systems is modelled as a series of transitions from one system microstate to another one and thermal equilibrium is reached via a random walk in the single-particle state space. We look at this dynamic process as a Markov chain satisfying the condition of detailed balance and propose a variant of the Monte Carlo Metropolis algorithm able to take into account indistinguishability of identical quantum particles. Simulations performed on different two-dimensional (2D) systems are revealed to be capable of reproducing the correct trends of the distribution functions and other thermodynamic properties. The simulations allow us to show that, away from the thermodynamic limit, a pseudo-Bose–Einstein condensation occurs for a 2D ideal gas of bosons.

Mechanical models of amplitude and frequency modulation

This paper presents some mechanical models for amplitude and frequency modulation. The equations governing both modulations are deduced alongside some necessary approximations. Computer simulations of the models are carried out by using available educational software. Amplitude modulation is achieved by using a system of two weakly coupled pendulums, whereas the frequency modulation is obtained by using a pendulum of variable length. Under suitable conditions (small oscillations, appropriate initial conditions, etc) both types of modulation result in significantly accurate and visualized simulations.

Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow.

In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms of macroscopic variables whose temperature dependence is proportional to the Boltzmann factor. A description of a workshop implementing the approach in the framework of an undergraduate course for engineering education and some preliminary results about its pedagogical relevance are then reported.

The Boltzmann probability as a unifying approach to different phenomena

We discuss a pedagogical approach to the role of the Boltzmann probability in describing the temperature dependence of three simple experimental situations. The approach has been experimented in an introductory course on statistical mechanics for undergraduate engineering students at University of Palermo.

Modelling Systems of Classical/Quantum Identical Particles by Focusing on Algorithms.

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having predictive validity are developed.

Collisions and Mechanical Wave Propagation in Elastic Rods

Some results from experiments intended to measure the propagation speed of sound waves produced by collisions between small bodies and metallic rods are analysed. Elementary models of elastic collision and of the reflection and transmission of waves at media boundaries are discussed and tested with experimental data, in the framework of a workshop on mechanical wave propagation that featured at the University of Palermo in a two-year graduate programme for prospective physics teachers and in courses for undergraduate engineering and physics students.

A problem-based approach to elastic wave propagation: the role of constraints

A problem-based approach to the teaching of mechanical wave propagation, focused on observation and measurement of wave properties in solids and on modelling of these properties, is presented. In particular, some experimental results, originally aimed at measuring the propagation speed of sound waves in metallic rods, are used in order to deepen the role of constraints in mechanical wave propagation. Interpretative models of the results obtained in the laboratory are built and implemented by using a well-known simulation environment. The simulation results are, then, compared with experimental data. The approach has been developed and experimented in the context of a workshop on mechanical wave propagation of the two-year Graduate Program for Physics Teacher Education at University of Palermo.