Visualizing the Doppler Effect

A special case of the relativistic Doppler effect, which occurs when light reflects from a moving mirror, is discussed. The classic formula for the Doppler shift is derived in a fully non-relativistic fashion using basic facts from geometry. The derivation does not involve Lorentz transformations, length contractions and time dilations, and therefore is conceptually simpler than the standard derivations in physics textbooks. This discussion can be useful for teaching introduc...

In the present work we intend to introduce a system based on VR (Virtual Reality) for examining analytical-geometric structures that occur in the study of mathematics and physics concepts in the last high school classes. In our opinion, an immersive study environment has several advantages over traditional two-dimensional environments (such as a book or the simple screen of a PC or tablet), such as the spatial understanding of the concepts exposed, more peripheral awareness a...

Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are also considered. The results, not mentioned in introductory Physics textbooks, are simple to derive and could be used in undergraduate courses.

Effectiveness of teaching digital signal processing can be enhanced by reducing lecture time devoted to theory, and increasing emphasis on applications, programming aspects, visualization and intuitive understanding. An integrated approach to teaching requires instructors to simultaneously teach theory and its applications in storage and processing of audio, speech and biomedical signals. Student engagement can be enhanced by engaging students to work in groups during the cla...

A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords. This paper shows that if three sounds are produced by three spatially separated sources, a "happy" sounding major chord can be observed as its "sad" sounding counterpart depending on the observer's velocity - a consequence of the well known D...

Convolution operation is indispensable in studying analog optical and digital signal processing. Equally important is the correlation operation. The time domain community often teaches convolution and correlation only with one dimensional time signals. That does not clearly demonstrate the effect of convolution and correlation between two signals. Instead if we consider two dimensional spatial signals, the convolution and correlation operations can be very clearly explained. ...

Based on the experience we have gained so far, as independent reviewers of Radioengineering journal, we thought that may be proved useful to publicly share with the interested author, especially the young one, some practical implementations of our ideas for the interactive representation of data using 3D/4D movement and animation, in an attempt to motivate and support her/him in the development of similar dynamic presentations, when s/he is looking for a way to locate the str...

Google Earth is a huge source of interesting illustrations of various natural phenomena. It can represent a valuable tool for science education, not only for teaching geography and geology, but also physics. Here we suggest that Google Earth can be used for introducing in an attractive way the physics of waves.

Teaching color science to Electrical Engineering and Computer Science (EECS) students is critical to preparing them for advanced topics such as graphics, visualization, imaging, Augmented/Virtual Reality. Color historically receive little attention in EECS curriculum; students find it difficult to grasp basic concepts. This is because today's pedagogical approaches are nonintuitive and lack rigor for teaching color science. We develop a set of interactive tutorials that teach...

The strange visual appearance of objects is one of the puzzling predictions of Einstein's relativity. This is mainly due to the distinction between measuring and seeing, where the former is described by the Lorentz Transformation and the latter considers the time light rays (emitted by each point on the object) take to reach the observer. We compute the apparent position of a point given its velocity, initial position, and observation time. The apparent speed of a point is ca...