# Oscillations and Waves: An Introduction

*Oscillations and Waves: An Introduction***, 2nd edition**

Richard Fitzpatrick

CRC Press (July 16, 2018)

299 pp.

ISBN 9781138479715

This is an undergraduate textbook on a course in physics or applied mathematics that is usually titled as Waves and Vibrations or Oscillations. Such a course is typically taught at the sophomore or junior level after the student has completed the introductory one-year course in physics and at least a semester-long course in ordinary and partial differential equation. The preface by the author explains the rationale for this book and its mathematical treatment. The subject matter is organized into 11 chapters, and each chapter has either the oscillation or wave word in its title to show consistency of the material covered. Each chapter has many unsolved exercises. A two-page bibliography is included at the end of this book where mostly the classical textbooks are listed. A subject index is given as well. It is claimed that the publisher’s website includes animations, widgets, and appendices, but the reviewer has been unable to conﬁrm this.

Chapter 1 on the “Simple Harmonic Oscillation” introduces mass-spring, L-C circuit, and pendulum oscillators without damping. Chapter 2 covers the “Damped and Driven Harmonic Oscillation” in the context of single degree of freedom mechanical and electrical systems; transient resonant and off-resonant responses are brieﬂy discussed. The “Coupled Oscillations” are addressed in chapter 3 using two and three degree of freedom systems. The string wave equation is then developed in chapter 4 under the “Transverse Standing Waves” using both lumped (with N beads) and the continuous 1-D structural methods; normal modes and initial value problems are then described for uniform string. Chapter 5 then extends the previous chapter under the “Longitudinal Standing Waves” for uniform elastic rod and organ pipe (plane wave) cases. The Fourier analysis is also brieﬂy mentioned in this chapter. The propagation of 1-D waves in then fully illustrated in chapter 6 on the “Travelling Waves” with examples to elastic rods, gases, strings, electrical transmission lines and electromagnetic waves in a very concise manner. The Doppler effect and transmission at the interfaces are also introduced.

The ﬁrst 6 (out of 11) chapters (as discussed above) are relatively short and occupy about 40 percent of the book. The mathematical treatment is simple, as vectors and complex algebra are not utilized. The ﬁnal 5 chapters (as discussed next) occupy about 60 percent of the book and form the core (and perhaps the intended purpose of the text), as more interesting topics emerge using slightly higher-level mathematics.

Chapter 7 on the “Multi-Dimensional Waves” discusses the special forms of the wave equation in Cartesian, cylindrical, and spherical coordinates; laws of geometric optics; and Fresnel relations, birefringence, electromagnetic wave polarization, and reﬂection phenomenon at the interface. The composition of harmonic waves of different frequencies is explained in chapter 8. On the “Wave Pulses” via the Fourier transform, a general solution of 1-D wave equation and amplitude-modulated wave and its bandwidth were discussed. Next, the book discusses the “Dispersive Waves” in chapter 9. Nonlinear relationship between frequency and medium properties is explained via electromagnetic waves (in magnetized and magnetized plasmas), Faraday rotations, waveguides, gravity waves, ship drag, and the like. The “Wave Optics” is covered in chapter 10 where single/multiple slit interference and diffraction are addressed along with 2-D Fourier transforms. This chapter discusses the Huygens-Fresnel principle and provides several diffraction examples along with a brief historical perspective. Finally, the book concludes with the “Wave Mechanics” in chapter 11. Here, the principles of quantum mechanics are explained including the probability interpretation of wave function and the uncertainty principle.

The reviewer is quite familiar with two other well-known books on the same topic: the ﬁrst by K. U. Ingard (1988), and the second by H. J. Pain (2005). In comparison, the Fitzpatrick book is shorter though more analytical. It is a rather old-fashioned book (in a good sense) since it does not include any solved examples or a summary of important formulas. Most of the exercises at the end extend the text material by asking the student to “show that” or “demonstrate that.”

Overall, this book is concise and precise and provides an excellent vehicle for introducing the essential aspects of oscillations and waves in a wide variety of physical systems. This textbook is, of course, recommended to undergraduate students, though practicing scientists and engineers may ﬁnd it worthwhile as well as a reference book.

Raj Singh

Emeritus Professor of Mechanical Engineering, Ohio State University

singh.3@osu.edu