Table of contents

Education in physics and geosciences can be effectively illustrated by the analysis of earthquakes and the subsequent propagation of seismic waves in the Earth. Educational seismology has matured to a level where both the hard- and software are robust and user friendly. This has resulted in successful implementation of educational networks around the world. Seismic data recorded by students are of such quality that these can be used in classic earthquake location exercises, for example. But even ocean waves weakly coupled into the Earth's crust can now be recorded on educational seismometers. These signals are not just noise, but form the basis of more recent developments in seismology, such as seismic interferometry, where seismic waves generated by ocean waves—instead of earthquakes—can be used to infer information about the Earth's interior. Here, we introduce an earthquake location exercise and an analysis of ambient seismic noise, and present examples. Data are provided, and all needed software is freely available.

Complex systems are characterised by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behaviour. Examples arise both in the physical and non-physical worlds. The study of complex systems forms a new interdisciplinary research area that cuts across physics, biology, ecology, economics, sociology, and the humanities. In this paper we review the essence of complex systems from a physicists' point of view, and try to clarify what makes them conceptually different from systems that are traditionally studied in physics. Our goal is to demonstrate how the dynamics of such systems may be conceptualised in quantitative and predictive terms by extending notions from statistical physics and how they can often be captured in a framework of co-evolving multiplex network structures. We mention three areas of complex-systems science that are currently studied extensively, the science of cities, dynamics of societies, and the representation of texts as evolutionary objects. We discuss why these areas form complex systems in the above sense. We argue that there exists plenty of new ground for physicists to explore and that methodical and conceptual progress is needed most.

The aerodynamic properties of a spinning table tennis ball were investigated using flight experiments. Using high-speed video cameras, the trajectory and rotation of an official ball (Nittaku 3-Star Premium), which was launched by a three rotor machine, were recorded. The drag and lift coefficients (C_D and C_L) were determined by analysing the video images. The measurements covered the speed and rotation range of typical table tennis shots in the form of the Reynolds number (Re) and dimensionless spin rate (SP), i.e. 3.0 × 10⁴ < Re < 9.0 × 10⁴ and 0 < SP < 1.0, and C_D and C_L were obtained as functions of Re and SP. We determined that the lift coefficient C_L is not a monotonically increasing function of SP. A deep valley of C_L was found around SP = 0.5, and the lift force exerted on a spinning ball almost vanished at Re = 9.0 × 10⁴ and 0.48 < SP < 0.5. These results qualitatively agree with the results from recent wind tunnel tests, but quantitative differences owing to the unsteady nature of the flight experiments remain. This anomaly in the lift coefficient should be called the 'lift crisis'.

In downhill alpine skiing, skiers often exceed speeds of 120 km h⁻¹, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s⁻¹, increasing to 185.8 N at 40 m s⁻¹. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.

Ultrabroadband electro-optic sampling is presented as an extremely sensitive technique to detect electric field amplitudes in free space. The temporal resolution provided by few-femtosecond laser pulses results in a bandwidth exceeding 100 THz, potentially covering the entire infrared spectral range. A pedagogic introduction to the operational principle of the method is given along the lines of a classical coherent input field and a zincblende-type electro-optic sensor. We then show that even the bare vacuum fluctuations of the electric field in the quantum ground state may be detected. This time-domain approach to quantum physics operates directly on sub-cycle scales where no local energy conservation holds. Therefore, signals may be obtained from purely virtual photons without amplification to finite intensity.

The momentum conservation law is applied to analyse the dynamics of a pulsejet engine in vertical motion in a uniform gravitational field in the absence of friction. The model predicts the existence of a terminal speed given the frequency of the short pulses. The conditions where the engine does not return to the starting position are identified. The number of short periodic pulses after which the engine returns to the starting position is found to be independent of the exhaust velocity and gravitational field intensity for a certain frequency of pulses. The pulsejet engine and turbojet engine aircraft models of dynamics are compared. Also the octopus dynamics is modelled. The paper is addressed to intermediate undergraduate students of classical mechanics and aerospace engineering.

It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the existence of a variational symmetry is equivalent to the existence of coordinates in the extended configuration space such that one of the coordinates is ignorable. The proof given here, which only requires multivariable calculus, provides an elementary derivation of the partial differential equation that determines the variational symmetries of a given Lagrangian, which is obtained in treatises on the Lie theory of symmetries of differential equations or of variational calculus.

Since Galileo used his pulse to measure the time period of a swinging chandelier in the 17th century, pendulums have fascinated scientists. It was not until Stokes' (1851 Camb. Phil. Soc.9 8–106)  (whose interest was spurred by the pendulur time pieces of the mid 19th century) treatise on viscous flow that a theoretical framework for the drag on a sphere at low Reynolds number was laid down. Stokes' famous drag law has been used to determine two fundamental physical constants—the charge on an electron and Avogadro's constant—and has been used in theories which have won three Nobel prizes. Considering its illustrious history it is then not surprising that the flow past a sphere and its two-dimensional analog, the flow past a cylinder, form the starting point of teaching flow past a rigid body in undergraduate level fluid mechanics courses. Usually starting with the two-dimensional potential flow past a cylinder, students progress to the three-dimensional potential flow past a sphere. However, when the viscous flow past rigid bodies is taught, the three-dimensional example of a sphere is first introduced, and followed by (but not often), the two-dimensional viscous flow past a cylinder. The reason why viscous flow past a cylinder is generally not taught is because it is usually explained from an asymptotic analysis perspective. In fact, this added mathematical complexity is why the drag on a cylinder was only solved in 1911, 60 years after the drag on a sphere. In this note, we show that the viscous flow past a cylinder can be explained without the need to introduce any asymptotic analysis while still capturing all the physical insight of this classic fluid mechanics problem.

A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.

We discuss the wobbling motion in a lens-shaped body rotation, focusing on the frequencies and the amplitude of nutation by filming the rotational motion and wobbling of the body. The friction coefficient of the surface is altered to examine its influence for two lenses with different curvature radii. MATLAB programs are developed to retrieve the Euler angles, which are graphed according to time. It is shown that the lens with a smaller curvature radius exhibits the wobbling effect in all cases, whereas the lens with a larger curvature radius shows such behaviour in limited circumstances. The study confirms that the friction coefficient has a negative linear correlation with the vertical axis declination amplitude with the R-squared value 0.878, showing that friction gives damping and causes smaller axis declination amplitudes. Negative linear correlation also exists with relation to the number of wobbles before the motion stops, where the R-squared value is 0.938, providing further evidence that friction and wobbling cause higher energy dissipation rates. The frequency of the wobbling motion only has a correlation with the curvature radius of the lens, showing no explicit correlation with the friction coefficient, with its R-squared value being 0.077. No losses of contact were observable in this motion. The overall process does not utilize particularly expensive apparatus and will be applicable for senior undergraduate students to experiment on and analyze the motion of a special situation regarding a rigid body that is both spinning and nutating.

A simple experiment is described where the tip of a metal ruler is used to strike a 50 g mass. Since the ruler is very flexible, the impact duration is much longer than usual, giving the impression that the ruler simply pushes the mass forward at low speed over a long distance. The tip of the ruler remains in contact with the mass throughout the impact. However, the impact is best described as a long duration collision with a coefficient of restitution (COR) greater than zero, despite the fact that the relative speed during and at the end of the collision is zero. If the mass rests on a table and if the ruler strikes the table before striking the mass, then the ruler bends and stores elastic energy. The result is a superelastic collision where the COR is greater than unity.

This paper shows that when students are introduced to the derivation of one of the most important physical formulas—the canonical distribution—they are exposed to assumptions which may be confusing because they contradict physical reality. The paper provides an alternative derivation of the canonical distribution. Our derivation takes into account internal physical processes in macrosystems leading to the canonical distribution and does not require any physically unjustified assumptions. The article is intended for teachers and students of statistical physics, and for general physicists.

Water, which is the habitat for a variety of living creatures, has a maximum density at 4.0 °C. This crucial property is considered to play a very important role in the biology of a lake and also has a close relationship with the areas of environmentology and geoscience. It would be desirable for students to confirm this important property of water themselves by carrying out simple experiments. However, it is not easy to detect the maximum density at 4.0 °C because the temperature dependence of the water density is very small close to its freezing point. For example, the density of water is 0.999 975 g cm⁻³ at 4.0 °C and 0.999 850 g cm⁻³ at 0.1 °C. The aim in this manuscript is to demonstrate a simple experiment to detect 4.0 °C as the temperature of maximum density, in which the time dependence of the water temperature is measured at several different depths by chilling the water surface. This is a simple experiment that can also be performed by high school students. We also present a mathematical model that can explain the results of this experiment.

With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information (${I}_{\rho }$) with the familiar energy levels of the quantum system. The corresponding momentum-space information (${I}_{\gamma }$) does not obey such a simple relationship with the energy spectrum. Our results for the product (${I}_{\rho }{I}_{\gamma }$) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor.40 1845)

Measurement of the Earth's magnetic field dip angle is a widely used experiment in most introductory physics laboratories. In this paper we propose a smartphone-aided setup that takes advantage of the smartphone's magnetometer sensor to measure the Earth's magnetic field dip angle. This set-up will help students visualize the vector nature of the Earth's magnetic field, especially high school and first year college students who are not quite experienced with vectors. This set-up is affordable and easy to use and could be easily produced by any high school or college physics instructor.

This work describes a very simple, low-cost experimental setup designed for measuring the force between permanent magnets. The experiment consists of placing one of the magnets on a balance, attaching the other magnet to a vertical height gauge, aligning carefully both magnets and measuring the load on the balance as a function of the gauge reading. A theoretical model is proposed to compute the force, assuming uniform magnetisation and based on laws and techniques accessible to undergraduate students. A comparison between the model and the experimental results is made, and good agreement is found at all distances investigated. In particular, it is also found that the force behaves as r⁻⁴ at large distances, as expected.

An experimental set-up for electrostatic measurement of ${\varepsilon }_{0}$, separate magnetostatic measurement of ${\mu }_{0}$ and determination of the speed of light $c=1/\sqrt{{\varepsilon }_{0}{\mu }_{0}}$ according to Maxwell's theory with percent accuracy is described. No forces are measured with the experimental set-up, therefore there is no need for a scale, and the experiment cost of less than £20 is mainly due to the batteries used. Multiplied 137 times, this experimental set-up was given at the Fourth Open International Experimental Physics Olympiad (EPO4) and a dozen high school students performed successful experiments. The experimental set-up actually contains two different pendula for electric and magnetic measurements. In the magnetic experiment the pendulum is constituted by a magnetic coil attracted to a fixed one. In the electrostatic pendulum when the distance between the plates becomes shorter than a critical value the suspended plate catastrophically sticks to the fixed one, while in the magnetic pendulum the same occurs when the current in the coils becomes greater than a certain critical value. The basic idea of the methodology is to use the loss of stability as a tool for the determination of fundamental constants.

Magnetic and electric fields can cause a charged particle to form interesting trajectories. In general, each trajectory is discussed separately in university physics textbooks for undergraduate students. In this work, a solution of a charged particle moving in a uniform electric field at right angles to a uniform magnetic field (uniform crossed electric and magnetic fields) is reported; it is limited to particle motion in a plane. Specific solutions and their trajectories are obtained only by varying the initial particle velocity. The result shows five basic trajectory patterns, i.e., straight line, sinusoid-like, cycloid, cycloid-like with oscillation, and circle-like. The region of each trajectory is also mapped in the initial velocity space of the particle. This paper is intended for undergraduate students and describes further the trajectories of a charged particle through the regions of electric and magnetic fields influenced by initial condition of the particle, where electromagnetic radiation of an accelerated particle is not considered.

The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for higher multipole moments. Moreover, a naive application of Gauss's law to the ideal dipole field appears to give an incorrect expression for the dipole's effective charge density. We derive a general result for the delta-function structure at the origin of an arbitrary ideal multipole field without using any advanced techniques from distribution theory. We find that the divergence of a singular vector field can contain a derivative of a Dirac delta function even if the field itself does not contain a delta function. We also argue that a physical interpretation of the delta function in the dipole field previously given in the literature is perhaps misleading and may require clarification. Both the explanation of and the resolution to this 'paradox' should be accessible to someone who has taken a graduate- or advanced undergraduate-level course in classical electrodynamics.

The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are obtained through the mapping from simple highly symmetric systems. In particular, the concept of multipole expansion is revisited from a point of view opposed to the usual one: the sources are distributed in a region far from the origin while the electrostatic potential is described at points close to it.

Maxwell's equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell's equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

We propose a laboratory experience aimed at undergraduate physics students to understand the main features of the photoelectric effect and to perform a measurement of the ratio h/e, where h is Planck's constant and e is the electron charge. The experience is based on the method developed by Millikan for his measurements of the photoelectric effect in the years from 1912 to 1915. The experimental setup consists of a photomultiplier tube (PMT) equipped with a voltage divider properly modified to set variable retarding potentials between the photocathode and the first dynode, and a set of LEDs emitting at different wavelengths. The photocathode is illuminated with the various LEDs and, for each wavelength of the incident light, the output anode current is measured as a function of the retarding potential applied between the cathode and the first dynode. From each measurement, a value of the stopping potential for the anode current is derived. Finally, the stopping potentials are plotted as a function of the frequency of the incident light, and a linear fit is performed. The slope and the intercept of the line allow one to respectively evaluate the ratio h/e and the ratio W/e, where W is the work function of the photocathode.

In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmission coefficients are introduced by calculating the normal-to-interface components of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave components that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely.

This paper presents a study of two commercial hollow-cathode lamps (HCLs) with the intention of demonstrating different phenomena in gas discharges. The optogalvanic effect in both HCLs is produced by a laser diode radiated at the wavelength that corresponds to neon transition 1s²–2p² at 659.89 nm. The voltage–current characteristics of the lamps are explained using a classical theory of hollow-cathode discharge, while the optogalvanic signal is treated as a small perturbation of the discharge current. For certain values of voltage self-sustained current oscillations are observed in one of the HCLs. In the same HCL laser-induced optogalvanic dumped oscillations are detected. A phenomenological model that includes the effective circuit parameters of the discharge is used to explain the oscillation characteristics.

This work reports the use of a smartphone's ambient light sensor as a valuable tool to study and characterize the efficiency of an optical source. Here, we have measured both luminous efficacy and efficiency of several optical sources (incandescent bulb and halogen lamp) as a function of the electric power consumed and the distance to the optical detector. The illuminance of LEDs as a function of the distance to the optical detector is characterized for different wavelength emissions. Analysis of the results confirms an inverse-square law of the illuminance with the detector–source distance and shows good agreement with values obtained by classical experiments. This experience will trigger awareness in students in terms of sustainability, light propagation and efficiency of different optical sources.

We present a simple and inexpensive method for determining the waist radius of a focused Gaussian laser beam. This method is motivated by the fact that if you focus the laser beam using a lens, the distance from the lens to the waist will vary slightly as the lens is moved along the beam-propagating direction. We show how the waist radius can be calculated from four large longitudinal lengths, measurable using a conventional millimeter-scale ruler. Analyzing the dependence of the calculated waist radius on these four measured lengths numerically shows that the accuracy of the calculated waist radius is mainly affected by the error in the relative shift in the distance from the lens to the waist position. The calculated waist radius for a real HeNe laser is close to the one measured directly using a commercial beam profiler with an error within 7%.

Usually, the reflection probability R(E) of a particle of zero energy incident on a potential which converges to zero asymptotically is found to be 1: $R(0)=1$. But earlier, a paradoxical phenomenon of zero reflection at zero energy ($R(0)=0$) has been revealed as a threshold anomaly. Extending the concept of half-bound state (HBS) of 3D, here we show that in 1D when a symmetric (asymmetric) attractive potential well possesses a zero-energy HBS, $R(0)=0$$(R(0)\ll 1)$. This can happen only at some critical values q_c of an effective parameter q of the potential well in the limit $E\to {0}^{+}$. We demonstrate this critical phenomenon in two simple analytically solvable models: square and exponential wells. However, in numerical calculations, even for these two models $R(0)=0$ is observed only as extrapolation to zero energy from low energies, close to a precise critical value q_c. By numerical investigation of a variety of potential wells, we conclude that for a given potential well (symmetric or asymmetric), we can adjust the effective parameter q to have a low reflection at a low energy.

We develop a simulation to facilitate the teaching of the photoelectric effect in an introductory course on quantum mechanics at undergraduate level. Through a Visual Basic program we describe the interaction of light with electrons in a metal conductor in the phenomenon according to the classical theory. The description includes both the microscopic interaction, as well as the predictions of the theory for the experimental results, arising from the microscopic scale. The predictions of the classical model are in stark contrast with the experimental results of a real photoelectric device.

To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.

An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.

Surface passivation is of great technological importance due to the increasing miniaturisation of electronic devices. It has been known for many years that under certain conditions surface states can form; when they do so in a quantum well (QW) the result is an unbound (i.e., evanescent) state in the QW. Such surface states are generally undesirable, so a good physical understanding of them is important. A simple single-p-orbital valence band model is used with two types of surface passivation to examine surface states in a QW: (1) an energy upshift added to the terminal atoms; and (2) explicit passivation by an s-orbital on each end of the QW. These models show these unbound/evanescent QW states can occur in both models; that in them the wavefunction is bound to the terminal atoms; and that the existence of these states is connected to the effective valence-band offset between the terminal atoms and the bulk QW.

'Das hätte ich einfacher sagen können (I could have said that more simply).' was Einstein's sigh when he had a chance to remark on his own derivation of the Lorentz transformation (LT) in the 1905 seminal paper. In fact, in a popular science exposition of the theory of relativity Einstein did provide such a simple derivation of the LT. It is a curious historical fact that the latter derivation was presented in 1916, while Einstein's remark was made in 1943. Was the 1916 derivation simple enough to relieve his sigh? Had he expected an even simpler derivation beyond his thoughts? In this paper, Einstein's simple derivation of the LT is revisited and analysed. We show that the LT can be obtained from a symmetry principle hidden in Einstein's logical reasoning. First, the relativity principle can be restated as a mirror principle based on the space–time exchange-inversion operation. Second, the assumed constancy of the speed of light (Einstein's second postulate) can be derived by using the velocity reciprocity property, which is a deductive result of the space–time homogeneity and the space isotropy. Therefore, Einstein could have presented his derivation of the LT more simply, thus turning Einstein's sigh of regret into a sigh of relief.

This paper describes a novel activity to model the dynamics of a Jupiter-mass, trans-Neptunian planet of a highly eccentric orbit. Despite a history rooted in modern astronomy, 'Planet X', a hypothesised hidden planet lurking in our outer Solar System, has often been touted by conspiracy theorists as the cause of past mass extinction events on Earth, as well as other modern-day doomsday scenarios. Frequently dismissed as pseudoscience by astronomers, these stories continue to draw the attention of the public by provoking mass media coverage. Targeted at junior undergraduate levels, this activity allows students to debunk some of the myths surrounding Planet X by using simulation software to demonstrate that such a large-mass planet with extreme eccentricity would be unable to enter our Solar System unnoticed, let alone maintain a stable orbit.

The Doppler effect is a shift in the frequency of waves emitted from an object moving relative to the observer. By observing and analysing the Doppler shift in electromagnetic waves from astronomical objects, astronomers gain greater insight into the structure and operation of our Universe. In this paper, a simple technique is described for teaching the basics of the Doppler effect to undergraduate astrophysics students using acoustic waves. An advantage of the technique is that it produces a visual representation of the acoustic Doppler shift. The equipment comprises a 40 kHz acoustic transmitter and a microphone. The sound is bounced off a computer fan and the signal collected by a DrDAQ ADC and processed by a spectrum analyser. Widening of the spectrum is observed as the fan power supply potential is increased from 4 to 12 V.

When connections between related observations and facts are not being made, introductory science classes can be perceived as an accumulation of disjointed equations with the risk of losing both students' interest as well as their grasp of the materials. In astronomy we have to walk a tightrope between being complete in our presentation of modern-day findings and skirting the surface of quantum mechanics. We introduce Wien's displacement law, Stefan–Boltzmann's law, Hubble's law, and we talk about the age of the Universe and when it first became transparent. The derivation of all these laws and their applications to get numbers out of observations requires knowledge of modern physics, knowledge that students have not acquired (yet), so we tend to choose to not make connections between them. In here, we offer an alternative approach to overcome these drawbacks: we make connections between the main tenets of the laws, such as the temperature dependence that enters Stefan–Boltzmann's law, and processes that students are familiar with, such as the acceleration of electrons. In doing so we reduce the number of disjointed facts presented to students, and we are able to relate equations to imagery that does not rely on faulty representations.

This paper focuses on results of an interview based survey of first-year university physics students, carried out within the EU Horizons in Physics Education (HOPE) project (http://hopenetwork.eu/). 94 interviews conducted in 13 universities have been analyzed to investigate the factors that inspire young people to study physics. In particular, the main motivational factor, which was proven to consist of personal interest and curiosity, was unfolded into different categories and detailed interest profiles were produced. The results are arguably useful to help academic curriculum developers and teaching personnel in physics departments to provide guidance to students in developing and focusing their interest towards specific sub-fields and/or to design targeted recruitment and outreach initiatives.

Development of validated physics surveys on various topics is important for investigating the extent to which students master those concepts after traditional instruction and for assessing innovative curricula and pedagogies that can improve student understanding significantly. Here, we discuss the development and validation of a conceptual multiple-choice survey related to magnetism suitable for introductory physics courses. The survey was developed taking into account common students' difficulties with magnetism concepts covered in introductory physics courses found in our investigation and the incorrect choices to the multiple-choice questions were designed based upon those common student difficulties. After the development and validation of the survey, it was administered to introductory physics students in various classes in paper–pencil format before and after traditional lecture-based instruction in relevant concepts. We compared the performance of students on the survey in the algebra-based and calculus-based introductory physics courses before and after traditional lecture-based instruction in relevant magnetism concepts. We discuss the common difficulties of introductory physics students with magnetism concepts we found via the survey. We also administered the survey to upper-level undergraduates majoring in physics and PhD students to benchmark the survey and compared their performance with those of traditionally taught introductory physics students for whom the survey is intended. A comparison with the base line data on the validated magnetism survey from traditionally taught introductory physics courses and upper-level undergraduate and PhD students discussed in this paper can help instructors assess the effectiveness of curricula and pedagogies which is especially designed to help students integrate conceptual and quantitative understanding and develop a good grasp of the concepts. In particular, if introductory physics students' average performance in a class is significantly better than those of students in traditionally taught courses described here (and particularly when it is comparable to that of physics PhD students' average performance discussed here), the curriculum or pedagogy used in that introductory class can be deemed effective. Moreover, we discuss the use of the survey to investigate gender differences in student performance.

More than 36 000 students and post-docs will be involved until 2025 in research at the Large Hadron Collider (LHC) mainly through international collaborations. To what extent they value the skills acquired? Do students expect that their learning experience will have an impact on their professional future? By drawing from earlier literature on experiential learning, we have designed a survey of current and former students at LHC. To quantitatively measure the students' perceptions, we compare the salary expectations of current students with the assessment of those now employed in different jobs. Survey data are analysed by ordered logistic regression models, which allow multivariate statistical analyses with limited dependent variables. Results suggest that experiential learning at LHC positively correlates with both current and former students' salary expectations. Those already employed clearly confirm the expectations of current students. At least two not mutually exclusive explanations underlie the results. First, the training at LHC is perceived to provide students valuable skills, which in turn affect the salary expectations; secondly, the LHC research experience per se may act as signal in the labour market. Respondents put a price tag on their learning experience, a 'LHC salary premium' ranging from 5% to 12% compared with what they would have expected for their career without such an experience at CERN.

We have developed a new introductory physics/chemistry programme that teaches advanced science topics and practical laboratory skills to freshmen undergraduate students through the use of student-led, bona fide research activities. While many recent attempts to improve college-level physics education have focused on integrating interactive demonstrations and activities into traditional passive lectures, we have taken the idea of active-learning several steps further. Working in conjunction with several research faculty at Binghamton University, we have created a programme that puts undergraduate students on an accelerated path towards working in real research laboratories performing publishable research. Herein, we describe in detail the programme goals, structure, and educational content, and report on our promising initial student outcomes.

A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.

We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the n-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one can greatly reduce the efforts to compute cumbersome angular integrals into straightforward combinatoric counts. This method is generalised into the cases in which such symmetries are present in subspaces. We further demonstrate the mechanism of the tensor-integral reduction that is widely used in various physics problems such as perturbative calculations of the gauge-field theory in which divergent integrals are regularised in $d=4-2\epsilon$ space–time dimensions. The main derivation is given in the n-dimensional Euclidean space. The generalisation of the result to the Minkowski space is also discussed in order to provide graduate students and researchers with techniques of tensor-integral reduction for particle physics problems.