Visualizing the Doppler Effect

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and Cherenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside--Feynman equations for calculating the magnetic and electric fields of a moving charge have been known for many decades, but it is only recently that the computing power to plot the fields of such a particle h...

Physlets are scriptable Java applets that can be used for physics instruction. In this article we discuss the pedagogical foundations of Physlet use and provide a sample of Physlet-based exercises that could be used to teach optics.

This is a short note to announce the availability of some movies that may be useful in classroom discussions on the photographic appearance of objects moving at relativistic speeds. The images are based on special relativity with no account taken of (other than to ignore) the effects of doppler shifts, intensity shifts or gravitational effects.

Physics Education Research (PER) studies have demonstrated that undergraduate students struggle with fundamental principles from Electromagnetism (EM) and Special Relativity (SR). However, few studies have approached the intersection of the two subjects: the role which EM played in inspiring the development of SR. To address this issue, this paper presents two simulations which highlight the fundamental role of electromagnetism in special relativity. The first simulation demo...

The Doppler effects for the reflected wave from a moving media are systemically analyzed in this paper. The theoretical formula for the Doppler shift in the left-handed material, which is described by Drude's dispersion model, is presented. This formula is examined by first-principles numerical experiments, which are in agreement with the theoretical results.

Modern physics is now a regular course for non-physics majors who do not have to take the accompanying laboratory. This lack of an experimental component puts the engineering students at a disadvantage. A possible solution is the use of computer simulations to add a constructivist element to the class. In this work, we present a set of computer simulations of fundamental experiments, a key to the teaching of modern physics, as well as their in-class implementation and assessm...

The convergence between astronomy and data sonification represents a significant advancement in the approach and analysis of cosmic information. By surpassing the visual exclusivity in data analysis in astronomy, innovative projects have developed software that goes beyond visual representation, transforming data into auditory and tactile displays. However, it has been evidenced that this novel technique requires specialized training, particularly for audio format data. This ...

This paper is presenting a set of laboratory classes to be taught as a part of a 1-year calculus-based physics class. It is composed out of 7 modules designed to bring together experiments and computer simulations (numerical simulations). Each module uses both simulations and experiments to address a phenomenon under study, and lasts for 3 weeks (21 weeks total for the whole set). Wolfram Mathematica is used for computer simulations. Topics are: Motion with a drag, Pendulum w...

Captain Einstein is a virtual reality (VR) movie that takes you on a boat trip in a world with a slow speed of light. This allows for a direct experience of the theory of special relativity, much in the same spirit as in the Mr. Tompkins adventure by George Gamow (1939). In this paper we go through the different relativistic effects (e.g. length contraction, time dilation, Doppler shift, light aberration) that show up during the boat trip and we explain how these effects were...

We present a study of student learning through the use of virtual reality. A software package is used to introduce concepts of special relativity to students in a game-like environment where users experience the effects of travelling at near light speeds. From this new perspective, space and time are significantly different to that experienced in everyday life. The study explores how students have worked with this environment and how these students have used this experience i...