Table of contents

Bagpipes are an ancient folk musical instrument, used as far back as ancient Greece. To this day, they are part of folk music in many countries and cultures. This paper deals with the modelling of the reed and melodic pipe (chanter) for bagpipes, focusing on tuning of the instrument. We present a theoretical model in the Geogebra software, which allows for qualitative simulating and visualizing the interaction between the reed blade and the air column of the pipe.

A non-returning boomerang can fly straight for over one hundred meters, but only if torques with a horizontal component are eliminated by careful shaping of the airfoil. An actuator disk model predicts that non-returning boomerangs must have a negative lift coefficient at both ends, in marked contrast to the returning boomerangs. Stability conditions are examined. The analysis of these ancient hunting weapons is, for the physics student, an instructive exercise in rotational dynamics.

Nother's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that a student of this field usually encounters. The derivation is based on the integration of the differential form dS = pdq − Hdt, where S is the action function, p is the momentum, and H the Hamiltonian, over a closed path.

We revisit the thermodynamic analysis of an isothermal ideal gas mixture enclosed within a cylinder and separated from the surrounding atmosphere by a movable and frictionless piston. When equilibrium conditions based on the chemical potentials of one or more species in the mixture are not satisfied at all times, which occurs for example for a chemical reaction with finite and non-zero reaction rates in the forward and reverse directions and for mass transfer of one species across a permeable membrane occurring at a finite and non-zero rate, an irreversibility is necessarily introduced into the system with a resulting increase in the entropy of the Universe. Consequently, when the piston is set in motion, it cannot oscillate indefinitely. The piston must again come to rest despite there not being any mechanical dissipative mechanisms, i.e. friction or viscous dissipation, nor a thermal dissipative mechanism, i.e. irreversible heat transfer, operating within the system. Only when the system is reversible, such that the entropy of the Universe remains constant at all times, will the piston oscillate indefinitely. 'Chemical damping,' or an irreversibility arising from nonequilibrium conditions on the chemical potential, provides another dissipative mechanism that has not yet been analyzed before.

In recent years, significant progress has been made in the development and application of artificial intelligence, spanning various fields and presenting powerful potential applications. The investigation of how to integrate the achievements of artificial intelligence with traditional physical problems has become a crucial task. Neural networks are considered as a pivotal technology of artificial intelligence, showcasing their distinctive ability to comprehend intricate nonlinear relationships through simulation and learning, and has showed exceptional performance in handling large-scale data and addressing inverse problems. This article begins by introducing the fundamental principles of neural networks, providing a detailed explanation of the process involved in constructing classical neural networks. A neural network was constructed on the MATLAB platform, and the practical application process was illustrated through lively demonstrations using simple examples. Tailored primarily for physics education, this article is designed to be suitable for undergraduate-level educational purposes. Through the integration of neural networks with practical inverse heat conduction problem, we not only provide a more interactive and dynamic learning experience but also enrich undergraduate students' comprehension and interest in relevant issues within higher education. This integrated teaching approach has the potential to propel interdisciplinary collaboration, nurturing innovation and advancement within the field of physics education.

The method of images to solve certain electrostatic boundary-value problems is taught worldwide in undergraduate-level physics courses. Though it is also possible to employ this technique for solving magnetostatic boundary value problems, examples of this usage are rarely found in textbooks or physics pedagogy literature. In particular, the problem of finding the field due to a magnetic dipole kept in front of a superconducting sphere is an interesting one, because (i) it helps the students to compare with the grounded conducting sphere image problem in electrostatics, and (ii) offers a greater degree of difficulty since the source is a dipole (vector), rather than an electric charge (scalar). The present work demonstrates an intuitive way of solving the problem. The case in which the source dipole is oriented radially with respect to the sphere is solved with a single dipole image. In the case of the transverse orientation of the source dipole, we model the dipole as a current loop. Then, we find the image of the radial and transverse current elements that satisfy the boundary conditions. Then, we show that this method can be used to deduce the form of the image dipoles when the dipole is oriented in the transverse direction. This method is very much intuitive and accessible for undergraduate-level students.

The method of cases of equilibrium is a lesser-known technique that effectively bridges theory and practice to derive fundamental natural laws. In this article, we will explain the method of equilibrium cases: we will introduce the historical motivation behind the development of this technique and outline the differences from the interpolation method. We will describe how to obtain an unprecedented equilibrium case — suitable for easy replication in the classroom — based on Ampère's motor phenomenon, which, along with two already known cases, will allow us to develop a contemporary approach to deducing Ampère's force between current elements. To our knowledge, this method is unknown in courses of experimental or mathematical methods of electrodynamics. The deduction section will require prior knowledge of calculus and unit vector notation.

Because the relativistic transformation of time involves spatial coordinates, multipole moments can take on very different values in relatively-moving inertial frames. As a related aspect, an infinite solenoid of finite cross-section will have non-zero time-varying electric fields outside its winding arising from the discrete charges carrying the solenoid currents. In the rest frame of the solenoid, the time averages of these time variations vanish and may be ignored. However, these time-varying electric fields have non-zero time averages in an inertial frame where the solenoid is moving perpendicular to its axis, and this non-zero time average plays an important role in the classical electromagnetic interpretation of the Aharonov–Bohm phase shift, which was treated in earlier work. Here we illustrate these ideas for a circular current loop, and then note their applicability to solenoids and toroids. The 'ideal magnetic moment' with no charges and no spatial extent is completely unphysical, and is seen to lead, in a moving inertial frame, to a different and incorrect average electric field from that where discrete charges are used and the radius of the magnetic moment is finite.

Moiré effect is a common phenomenon that arises from a slight mismatch in the period of two structures. A prominent example in the microscopic world is magic-angle twisted bilayer graphene (MATBG). In this work, to enhance undergraduate students' advanced learning of interference and diffraction, we reproduced the microscopic structure of MATBG on a macroscopic scale by creating hexagonal structured masks. By designing a suitable optical path, we were able to realize the optical diffraction of this macrostructure. The results revealed two additional periodic diffraction patterns in the twisted double-layer masks, which are relevant to the moiré effect. Through theoretical derivation and computer simulation, we explained the observed diffraction patterns, which matched well with the experiments. This designed project not only improves students' knowledge in optics and laboratory operation skills, but also deepens their comprehension of moiré effect and crystal diffraction, showcasing its potential for further expansion and application in undergraduate physics education.

The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 Eur. J. Phys.35 015006) introduced a Laplace-transform-based method to solve the stationary Schrödinger equation for various potentials. However, their approach contains critical methodological flaws: the authors disregard essential boundary conditions and apply the residue theorem incorrectly in the inverse transformation process. These errors ultimately cancel out, leading to correct results despite a flawed derivation. In this paper, we revisit the use of the Laplace transform for the one-dimensional Schrödinger equation, clarifying correct practices in handling boundary conditions and singularities. This analysis offers a sound and consistent framework for the application of Laplace transforms in stationary quantum mechanics, underscoring their educational utility in quantum mechanics coursework.

The problem of atomic ionization by the sudden absorption of momentum by its nucleus is studied. By means of a simple one dimensional model we obtain analytical expressions for the re-capture and ionization probabilities. Simple integral formulas for the evaluation of the time evolution of the electronic state are given. Analytical expressions for the ionization probabilities show structures found in realistic three dimensional collisional problems, such as capture probability (by the recoil nucleus) and the binary ionization peak.

In both Upper Secondary School and first-level university courses, Newtonian gravitation is typically taught with a primary focus on theoretical aspects, particularly on solving the two-body problem. The solution is claimed reproduce Kepler's empirical laws, but little attention is given to the details of its validation. In the past, the emphasis on theory could be justified by the technical difficulties associated with accessing and analyzing data. Today, however, the availability of open-access data and advanced computational tools makes it feasible to construct empirical evidence for Newtonian gravitation, even within classroom settings. This work revisits the arguments Newton himself used to support his theory and replicate the validation process through a series of activities designed for educational purposes. This approach includes analyzing astrophotographic and mareographic data, along with revisiting Aristarchus of Samos's method for measuring the distance to the Moon through eclipse analysis.

We investigated how students apply the concept of circulation when faced with problems related to the Ampère–Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed their responses using phenomenography. We complemented our research by conducting interviews with 12 students. The results show that students tend to think that they can only use the magnetic field circulation to calculate magnetic fields if the curve used is symmetric, and that they do not take into account the shape of the magnetic field lines when applying it. We also find that some students believe that a variable electric field must cross the entire Amperian curve in order to apply Ampère–Maxwell's law and find the magnetic field.

A simple analytic model for climate and climate change suitable for physics education in upper secondary and tertiary education is presented. It falls into the class of zero-dimensional energy balance models, comprises five independent variables and uses mathematical techniques only at a moderate level. It allows for the definition and discussion of key concepts of climate science such as radiative forcing, climate sensitivity and feedback factors, including an elementary feedback analysis for the four most important fast climate feedbacks. To round off the text, it is briefly shown how the model can be coupled to the ocean as a heat reservoir, providing a rough estimate for the characteristic time scales of climate change. The analysis is formulated rigorously in terms of the model variables.

This study introduces a straightforward approach to determine Planck's constant in an undergraduate course at the college or university level through the analyses the current–voltage (I–V) characteristic of a tungsten filament bulb. Unlike conventional methods, this analysis does not require the use of a color filter or an additional photodiode to select a specific wavelength or measure the emitted energy density from the filament. The temperature of the filament was computed by measuring the resistance of the filament. The obtained temperature and the input power of the filament are then used to estimate the emissivity of the filaments using Stefan–Boltzmann's law, which is found to be lower than that of a perfect black body, i.e. unity. Therefore, the radiation emitted from the tungsten filament can be classified as gray radiation. The maximum energy density (intensity) of the emitted radiation is determined by calculating the consumed power of the filament. Finally, the obtained values of temperature, Stefan's constant, and the intensity of the emitted radiations are used to calculate Planck's constant. The calculated value of Planck's constant is found to be 6.102 × 10⁻³⁴ Js, which closely matches the standard value of Planck's constant (6.626 × 10⁻³⁴ Js). This close correlation between the two values validates the effectiveness of the present method.

Problem-solving in physics and mathematics has been characterised in terms of five phases by Schoenfeld, and these have previously been used to describe also online and blended behaviour. We argue that expanding the use of server logs to make detailed categorisations of student actions can help increase knowledge about how students solve problems. We present a novel approach for analysing server logs that relies on network analysis and principal component analysis. We used the approach to analyse student interactions with an online textbook that features physics problems. We find five 'components of behavioural structure': Complexity, Linear Length, Navigation, Mutuality, and Erraticism. Further, we find that problem-solving sessions can be divided into four overarching groups that differ in their Complexity and further into ten clusters that also differ on the other components. Analysing typical sessions in each cluster, we find ten different behavioural structures which we describe in terms of Schoenfeld's phases. We suggest that further research integrates this approach with other methodological approaches to get a fuller picture of how learning strategies are used by students in settings with online features.

Laser absorption spectroscopy, grounded in the Lambert–Beer law, stands out as a prevalent non-destructive testing method within optical gas sensing technology. It finds extensive applications across atmospheric environment monitoring, industrial process control, combustion diagnosis, and biomedicine. Within this study, a pioneering gas absorption spectrum detection system is introduced, leveraging LabVIEW programming and tunable diode laser absorption spectroscopy. This system is tailored for college physics education, enabling undergraduates to grasp the fundamental workings of optical gas sensing technology. Methane (CH₄) is selected as the target gas molecule for its relevance in environmental dynamics and the push towards carbon neutrality. Investigative experiments delve into diverse spectral line parameters impacting the gas absorption signal profile, as prescribed by the theoretical underpinnings of laser spectroscopy. The teaching methodology proposed herein blends theoretical concepts with hands-on experimentation, fostering a deep student interest in the exploration of gas sensing technologies within the college physics domain.

This article deals with the context of seismology and its relevance to the teaching of physics in a modern and highly motivating way. A modular system called Raspberry Shake RS1D is presented, which is capable of detecting earthquakes as well as everyday vibrations. The Raspberry Shake 1D Vertical Motion Seismograph combines a Raspberry Pi mini-computer, a vertical geophone, a 24-bit digitizer and a near-real-time (miniSEED) data transmission. While the Raspberry Shake is a low cost professional and already well known tool for seismologists, we as physicists 'simply' used that computer-based measurement system. We describe how the seismograph works. We present the detection of ground motion from earthquakes as well as from everyday vibrations using selected examples. Thereby, we focus on teaching physics in the context of seismology, presenting didactic ideas for learning about acoustics, for utilizing measurement systems and for applying scientific methods. This article is especially relevant for teaching undergraduate students. Basic facts about earthquakes that are essential for the study of the seismic phenomena discussed in this article are conveyed.

Capillarity refers to the ability of a liquid to move within narrow spaces such as tubes and pores with reduced diameters or between two oblique plates with a very small angle between them. It is well known that the height a liquid can reach due to capillarity is directly related to the values of the surface tension, the density, and the contact angle. In this investigation, a study is conducted on the dependence of these properties on the glycerol concentration in an aqueous solution and on the water temperature. The experimental device used is a capillary formed by two oblique glass plates, which allows for the direct observation of the liquid height variation as a function of the separation angle between the plates. This phenomenon is studied using Jurin's law, widely used in the study of capillarity. The results are explained using the Connors–Wright surface tension model and the Eötvös rule. The experiment is very low cost and easy to implement in undergraduate science laboratories, making it useful for exploring the capillarity phenomenon of liquids.

In 2010, the International Young Physicists' Tournament (IYPT) was introduced to China as an exploratory practical physics activity for young students. Over the past decade, accompanied by annual competitions, students have gradually come to appreciate this research and learning approach around open-ended problems. Since 2018, we have established a lab focused on inquiry-based learning around the annual IYPT problems and redesigned introductory physics laboratory course, serving a large number of first-year students. Since then, the teaching team has continuously refined the teaching process and arrangements. This article focuses on introducing the entire teaching program and student feedback for the redesigned introductory physics laboratory that incorporating IYPT Problems with inquiry-based physics experimental teaching methods to serve a large number of students. We hope to provide valuable references for other institutions.

We make some crucial remarks about the recent presentation by Cross [Eur. J. Phys. 44 (2023) 055 006] for pedagogical purposes considering the above mentioned results. Most of the statements relevant to figure 2 of the above mentioned paper are of doubt to us. Our proposed amendments or corrections are useful for researchers as well as undergraduate physics students.