Table of contents

In this paper we present a non-intrusive experimental approach for obtaining a two-dimensional velocity distribution around a 22 mm diameter circular cylinder mounted in a water tunnel. Measurements were performed for a constant Reynolds number of 7670 using a commercial standard particle image velocimetry (PIV) system. Different flow patterns generated behind the circular cylinder are discussed. Both instantaneous and time-averaged velocity distributions with corresponding streamlines are obtained. Key concepts in fluid mechanics, such as contra-rotating vortices, von Kármán vortex street, and laminar-turbulent flow, are discussed. In addition, brief historical information pertaining to the development of flow measurement techniques—in particular, PIV—is described.

In this paper, an energy pumping mechanism for locomotion is analysed. The pumping is accomplished by exerting forces perpendicular to the direction of motion. The paper attempts to demonstrate an interesting application of the classical mechanics to two sporting events: a person skating in a half pipe and a person travelling on a level surface on a skateboard. The equations of motion based on simplified mechanical models are derived using the Lagrange mechanics. The energy-pumping phenomenon is revealed through numerical simulations with simple pumping actions. The result presented in this paper can be used as an interesting class project in undergraduate mechanics or physics courses. It also motivates potential new applications of energy pumping in many engineering fields.

In this paper, we present an interesting experiment to turn the vibratory light from an incandescent light bulb into audible sound. Inspired by research on the photoacoustic effect (PAE) using lasers, we construct a similar device in an undergraduate physics laboratory with everyday articles including light bulbs, glass beakers and soot. Using our device, a distinct sound is detected and analysed experimentally. Particular attention is paid to the attenuation effect of the acoustic signal, which can be explained by modifying the existing theory and using the adiabatic boundary condition according to the incident light source we use. This demonstration is a comprehensive experiment with the combination of sound, light and heat. The modification on the model can help undergraduate students gain an intuitive understanding of different boundary conditions.

The selection and application of coordinate systems is an important issue in physics. However, considering different frames of references in a given problem sometimes seems un-intuitive and is difficult for students. We present a concrete problem of projectile motion which vividly demonstrates the value of considering different frames of references. We use this example to explore the effectiveness of video-based motion analysis (VBMA) as an instructional technique at university level in enhancing students' understanding of the abstract concept of coordinate systems. A pilot study with 47 undergraduate students indicates that VBMA instruction improves conceptual understanding of this issue.

The hanging chain is a very instructive system for demonstrating more advanced methods and ideas for the analysis of normal modes of one-dimensional systems, beyond the standard ordinary (horizontal) string. Accordingly, the normal modes of the hanging chain are analysed with several cases of boundary conditions and are compared to the ordinary vibrating string.

Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels.

Type Ia supernovae (SNe Ia) have been intensively investigated due to their great homogeneity and high luminosity, which make it possible to use them as standardizable candles for the determination of cosmological parameters. In 2011, the physics Nobel prize was awarded 'for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.' This is a pedagogical article, aimed at those starting their study of that subject, in which we dwell on some topics related to the analysis of SNe Ia and their use in luminosity distance estimators. Here, we investigate their spectral properties and light curve standardization, paying careful attention to the fundamental quantities directly related to the SNe Ia observables. Finally, we describe our own step-by-step implementation of a classical light curve fitter, the stretch, applying it to real data from the Carnegie Supernova Project.

The thermal efficiency of a heat engine is of primary interest in introductory thermodynamics courses. This study presents a simple method to quantitatively distinguish the factors that cause the thermal efficiency of a heat engine to be less than unity. These factors are the nonzero reference point, external irreversibilities and internal irreversibilities. Next, the difference between the present method and the existing second-law efficiency method for evaluating the influence of irreversibility is discussed. Then, an example of an actual heat-engine cycle is given to demonstrate the feasibility and effectiveness of the presented method. Finally, some remarks on the relevance of the three factors to our attitude toward life are presented.

The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated with a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we do not consider very ad hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz invariance or locality above the cut-off, in which case the cut-off has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz invariance spontaneously.

I present a didactical project, introducing the concept of information with all its interdisciplinary ramifications to students of physics and the neighbouring sciences. Proposed by Boltzmann as entropy, information has evolved into a common paradigm in science, economy, and culture, superseding energy in this role. As an integrating factor of the natural sciences at least, it lends itself as guiding principle for innovative teaching that transcends the frontiers of the traditional disciplines and emphasizes general viewpoints. Based on this idea, the postgraduate topical lecture presented here is intended to provide a firm conceptual basis, technically precise but versatile enough to be applied to specific topics from a broad range of fields. Basic notions of physics like causality, chance, irreversibility, symmetry, disorder, chaos, complexity can be reinterpreted on a common footing in terms of information and information flow. Dissipation and deterministic chaos, exemplifying information currents between macroscopic and microscopic scales, receive special attention. An important part is dedicated to quantum mechanics as an approach to physics that takes the finiteness of information systematically into account. Emblematic features like entanglement and non-locality appear as natural consequences. The course has been planned and tested for an audience comprising, besides physicists, students of other natural sciences as well as mathematics, informatics, engineering, sociology, and philosophy. I sketch history and objectives of this project, provide a resume of the course, report on experiences gained teaching it in various formats, and indicate possible future developments.

This paper studies the oscillation properties of a simple pendulum immersed in a viscous liquid. A nonlinear equation of motion for the pendulum is first established by considering both viscous damping and quadratic damping, and solved by using the improved averaging method. Then a relationship between the oscillation period and the viscosity of liquid is derived. The experimental data obtained are consistent with the theoretical prediction, which also suggests a new approach to measure the liquid viscosity. We believe that this paper may be helpful for broadening teaching content for the simple pendulum and for better understanding the vibration of an object in liquids in some applications.

The magnetic vector potential (Coulomb gauge) is commonly introduced in magnetostatic chapters of electromagnetism textbooks. However, what is not typically presented are the infinite subsets of the Coulomb gauge associated with differential current elements. This work provides a comparison of various differential magnetic vector potentials, differential magnetostatic potential energies, as well as differential current element forces as a collective work not available elsewhere. The differential magnetic vector potential highlighted in this work is the Coulomb–Ampère gauge corresponding to the centrally conservative Ampère current element force. The centrally conservative force is modeled as a mean valued continual exchange of energy carrier mediators accounting for both the differential magnetostatic potential energy and Ampère current element force of two differential current elements.

In this paper we propose a mathematical model to describe a theoretical device able to simulate an inverse-square force on a test mass moving on a horizontal plane. We use two pulleys, a counterweight, a wire and a smooth rail, in addition to the test mass. The tension of the wire (i.e. the attractive force on the test mass) is determined by the position of a counterweight free to move on a rail placed under the plane. The profile of the rail is calculated in order to obtain the required Newtonian force. Details of this calculation are reported in the paper, and numerical simulations are provided in order to investigate the stability of the orbits under the effect of the main friction forces and other perturbative effects. This work points out that there are some criticalities intrinsic to the apparatus and gives some suggestions about how to minimize their impact.

Observation of conoscopic figures through a special microscope is widely used as an experimental method for determination of optical properties of anisotropic materials. The conoscopic figure appears when a divergent light passes through an anisotropic material sandwiched between crossed polarizers. The complex pattern of bright and dark areas appears due to different polarization states of light. The pattern gives information about optical axes and birefringence of the material and allows for deduction of microscopic structures at the origin of such properties. Due to the complexity of the figure, the method is often used following recipes. This contribution presents a series of experiments that provide students with experiences needed for construction and comprehension of optical phenomena that contribute to the complexity of the conoscopic figure.

In this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and thermodynamical problems are used as a storyline to introduce the mathematical formalism required to clarify the distinction between the uniqueness and multiplicity of equilibrium solutions and the critical states of a nonlinear physical problem, as well as to illustrate how these novel numerical continuation techniques are implemented in practice. The paper provides simple numerical Matlab codes that are easily adaptable to other problems, as well as updated software and literature resources.

The rigorous proof of the orthogonality integral $\int _{0}^{\infty }\rho \;{{J}_{\nu }}(k\rho ){{J}_{\nu }}(k^{\prime} \rho )\;{\rm d}\rho =\frac{\delta (k-k^{\prime} )}{k}$, for $\nu \geqslant -1,$ is laborious and requires the use of mathematical techniques that, probably, are unfamiliar to most physics students, even at the graduate level. In physics, we are used to the argument that it may be proved by the use of Hankel transforms. However, the logic of the matter is the opposite, i.e., the existence of the inverse Hankel transform is a consequence of the orthogonality integral. The goal of this work is to prove this integral without circular reasoning. In this paper, using elementary properties of Bessel functions, we give a simple analytical derivation of this integral for the case where ν is an integer, zero, or half-integer not less than $-1/2$. Then, using the asymptotic behaviour of ${{J}_{\nu }}(x)$, we extend the result to any $\nu \geqslant -1$. This work is of a pedagogical nature. Therefore, to add educational value to the discussion, we do not skip the details of the calculations.

A piezoelectric ceramic resonator is used for the 'electrical' measurement of elastic properties, i.e. Young's modulus and ultrasonic wave velocity in metallic materials. Piezoelectric response is precisely calculated for the piezoelectric ceramic ring fixed at the end of a metallic rod. The piezoelectric ring serves as both an actuator as well as a sensor. The experimental setup and method of measurement using higher overtones is explained in detail and practically demonstrated for a set of different metallic materials. Young's moduli and ultrasonic wave velocities are measured within 3% relative error. The presented method is suitable for an advanced engineering class or physics laboratory training.

Due to reversibility of light rays, th.e thin-lens equation (TLE) is symmetric under the exchange of the object distance and the image distance. To measure the focal length of a converging lens, the displacement method (or Besselʼs method) utilizes the two different configurations of the real object, the converging lens and the real image which correspond to the two symmetric solutions of the TLE. Theoretically, we show that this method can be generalized to all possible pairs of symmetric solutions of the TLE for both converging and diverging lenses.

This paper revisits the famous Foucaultʼs pendulum by highlighting two often-disregarded aspects in mechanics courses. The first one concerns the existence of a local accelerated reference frame to express the law of dynamics without the Coriolis force. The second aspect deals with the geometrical phase that appears in pendulum dynamics. This last point, which could appear banal, should be related to analogous consideration in quantum physics. It is also linked to vectorial parallel transport of the pendulum angular momentum eigenvector. Numerical simulations with MATLAB are proposed.

Encouraging 'active learning' in the large lecture theatre emerges as a credible recommendation for improving university courses, with reports often showing significant improvements in learning outcomes. However, the recommendations are based predominantly on studies undertaken in mechanics. We set out to examine those claims in the thermodynamics module of a large first year physics course with an established technique, called interactive lecture demonstrations (ILDs). The study took place at The University of Sydney, where four parallel streams of the thermodynamics module were divided into two streams that experienced the ILDs and two streams that did not. The programme was first implemented in 2011 to gain experience and refine logistical matters and repeated in 2012 with approximately 500 students. A validated survey, the thermal concepts survey, was used as pre-test and post-test to measure learning gains while surveys and interviews provided insights into what the 'active learning' meant from student experiences. We analysed lecture recordings to capture the time devoted to different activities in a lecture, including interactivity. The learning gains were in the 'high gain' range for the ILD streams and 'medium gain' for the other streams. The analysis of the lecture recordings showed that the ILD streams devoted significantly more time to interactivity while surveys and interviews showed that students in the ILD streams were thinking in deep ways. Our study shows that ILDs can make a difference in students' conceptual understanding as well as their experiences, demonstrating the potential value-add that can be provided by investing in active learning to enhance lectures.

This paper presents educational experiments, in which propagation and interference of elastic waves with a frequency of 25–30 kHz in thin plates are analysed. For obtaining these waves a magnetostriction radiator and an ultrasonic generator are used. The described devices are available for production in an educational laboratory. A standing flexural wave is visualized with dry fine powder. The powder accumulates in the nodes of the standing wave, and the distance between the nodes is equal to a half-wavelength. The unexpected phenomenon of visualization of a progressing flexural wave with powder is considered. The observed pattern consists of concentric circles, the smallest distance between which is equal to the wavelength. A simple theory of this phenomenon is offered. Measurements of the length and the velocity of the flexural wave in the plate are carried out. It is shown that the experimental results are well coordinated with the theory. The material of this paper is topical for students, graduate students and physics lecturers.

In classical electrodynamics all the measurable quantities can be derived from the gauge invariant Faraday tensor ${{F}_{\alpha \beta }}$. Nevertheless, it is often advantageous to work with gauge dependent variables. In [2, 4] and [8], and in the present paper too, the transformation of the vector potential in the Lorenz gauge to that in the Coulomb gauge is considered. This transformation can be done by applying a projection operator that extracts the transverse part of spatial vectors. In many circumstances the proper projection operator is replaced by a simplified transverse one. It is widely held that such a replacement does not affect the result in the radiation zone. In this paper the action of the proper and simplified transverse projections will be compared by making use of specific examples of a moving point charge. It will be demonstrated that whenever the interminable spatial motion of the source is unbounded with respect to the reference frame of the observer the replacement of the proper projection operator by the simplified transverse one yields, even in the radiation zone, an erroneous result with error which is of the same order as the proper Coulomb gauge vector potential itself.