Arnt Inge Vistnes - Physics of Oscillations and Waves

The University of Oslo in Norway is one of the first universities to introduce numerical methods as an integral part of almost all mathematically oriented courses for science students (first attempts started in 1997). This created the need for textbooks in physics covering all the topics included in the syllabus. There were many textbooks on oscillations and waves on the market, but none adhered well with the learning objectives we adopted.

The Norwegian version of this book was originally written in 2008 for use in the course FYS2130 Svingninger og blger (Oscillations and Waves) and has undergone many revisions and expansions since then. The course is given in the fourth semester to students enrolled in the Department of Physics at the University of Oslo. These students have taken courses in Python programming, classical mechanics and electromagnetism, but have had limited education in oscillations and wave phenomena.

In the present book, I have mostly adhered to traditional descriptions of the phenomena; however, I have also tried to point towards potential limitations of such descriptions. When appropriate, analogies between different phenomena are drawn.

The formalism and phenomena are treated quite differently from section to section. Some sections provide only qualitative descriptions and thus only a superficial or introductory understanding of the topics while other sections are more mathematical and demanding. Occasionally, the mathematical derivations are not essential to understand the material, but are included to show the connection between basic physical laws and the phenomena discussed in the text.

Principles from numerical methods are employed as they permit us to handle more realistic problems than pure analytical mathematics alone, and they facilitate to obtain a deeper understanding of some phenomena.

Program codes are given, ready to use, and is a tool for further exploration of the phenomena that are covered. Our experience from teaching this topic to students over years is that, numerical methods based on hands-on computer code development expand the experimental attitude and facilitate the learning process.

We try in this book to emphasize how so-called algorithmic thinking can improve understanding. As a personal example, the algorithm for calculating how a wave evolves over time has given me a much deeper understanding of the wave phenomena than by working with analytical mathematics over years. Another example is the realization that all variants of classical interference and diffraction can be calculated using a single computer program, demonstrating not only that numerical methods are powerful, but also that the underlying physical mechanism is identical in all these cases.

We have made an effort to ensure a logical and reader-friendly structure of the book. Especially important parts of the core material in the text are marked by coloured background, and various examples show how the core material can be used in different contexts. Supplementary information and comments are given in small print. Learning objectives point to the most important sections of each chapter. Most of the chapters include suggestions to further reading.

There are three types of exercises in the book. The first type of exercise consists of a list of concepts in each chapter that can be used by students in various ways for active learning. Thereafter follow comprehension/discussion questions and more regular problems often including calculations. Best learning outcome is achieved by trying all the three types of tasks, including oral discussions when working with understanding concepts and the comprehension/discussion questions. The problems used in the exercises are taken from daily life experiences, in order to demonstrate how physics is relevant in many aspects of our everyday life.