Waves and Oscillations in Nature: An Introduction, 1st Edition (Hardback) book cover

Waves and Oscillations in Nature

An Introduction, 1st Edition

By A Satya Narayanan, Swapan K Saha

CRC Press

551 pages | 129 B/W Illus.

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Waves and oscillations are found in large scales (galactic) and microscopic scales (neutrino) in nature. Their dynamics and behavior heavily depend on the type of medium through which they propagate.

Waves and Oscillations in Nature: An Introduction clearly elucidates the dynamics and behavior of waves and oscillations in various mediums. It presents different types of waves and oscillations that can be observed and studied from macroscopic to microscopic scales. The book provides a thorough introduction for researchers and graduate students in assorted areas of physics, such as fluid dynamics, plasma physics, optics, and astrophysics.

The authors first explain introductory aspects of waves and electromagnetism, including characteristics of waves, the basics of electrostatics and magnetostatics, and Maxwell’s equations. They then explore waves in a uniform media, waves and oscillations in hydrodynamics, and waves in a magnetized medium for homogeneous and nonhomogeneous media. The book also describes types of shock waves, such as normal and oblique shocks, and discusses important details pertaining to waves in optics, including polarization from experimental and observational points of view. The book concludes with a focus on plasmas, covering different plasma parameters, quasilinear and nonlinear aspects of plasma waves, and various instabilities in hydrodynamics and plasmas.


"The range of topics covered in this introduction for researchers and reference volume can be summarized by a list of the nouns appearing just before the word 'waves' in the table of contents: harmonic, electromagnetic, longitudinal, dispersive, hydrodynamic, surface, Poincare and Kelvin, Lamb and Rayleigh, Rossby, MHD, sound, Alfven, magnetoacoustic, solitary, gravity (meaning the kind in a fluid with gravitation as the restoring force), inertial, and shock. … Specific astronomical applications appear in discussions of radio antennae, ionospheric processes, and shock waves in the Sun, in connection with solar flares and coronal mass ejections. … Indeed the bibliography is one of the joys of this treatise, including original papers by Hertz, Strutt (Rayleigh to most of us), Brillouin, Compton, Planck, Doppler, Young, Michelson & Morley, Kirchhoff, Babinet, Coulomb, Hall, Oersted, Thompson, Poynting, Taylor, Heisenberg, Einstein, Bohr, Schrodinger, and Poincare. … On the plus side, the numbers used in some MHD wave problems are appropriate for the solar corona."

—Virginia Trimble, from The Observatory, February 2016

"… Since the authors present a very rich compendium on waves and oscillations, the book is not only of an introductory character, but rather a kind of vademecum. It leads the reader through the very rich domain of oscillations and waves, starting from the most elementary simple ones and collecting nearly all chapters in physics, where the problems of oscillations and wave-like phenomena occur. … The work is an excellent contribution with special aims. Namely, it offers an extremely broad treatment of the problems of oscillations and waves throughout the whole of physics. … It is meant to be accessible to undergraduates, though readers among the 'elder' researchers also may make practical use of it. This is because the style of the presentation is rather concise; it does not spend too much space for the detailed explanation of the starting points of the cited results. In summary, we are persuaded that this work will be quite valuable for beginners (after obtaining some basic experience) as well as for working professionals."

—Ivan Abonyi (Budapest), from Zentralblatt MATH 1323 — 1

Table of Contents

Introduction to Waves and Oscillations


What Is a Wave

Harmonic Wave

Monochromatic Fields

Intensity of Waves



Electromagnetic Waves



Time-Varying Fields

Maxwell’s Equations

Energy Flux of Electrodynamics

Electromagnetic Field Equations


Waves in a Uniform Media


Simple Harmonic Oscillation

Damped Oscillations

Coupled Oscillations

One-Dimensional Wave Equation: D’Alembert’s Solution

Helmholtz Equation

Normal Mode Eigenvalue Problem

Longitudinal Waves

Traveling Waves

Dispersive Waves


Hydrodynamic Waves


Basic Equations

Small-Amplitude Waves

Gravity Waves

Linear Capillary and Gravity Waves

Surface Waves Generated by a Local Disturbance in the Field

Klein–Gordon Equation

Shallow Water Waves

Boussinesq Equation

Finite Amplitude Shallow Water Waves (Nonlinear Aspects)

Plane Waves in a Layer of Constant Depth

Poincaré and Kelvin Waves

Lamb and Rayleigh Waves

Inertial Waves

Rossby Waves

Forced Stationary Waves in the Atmosphere

Solitary Waves: KdV Equation

MHD Waves in a Uniform Media

Basic Equations

Sound Waves

Alfven Waves

Shear Alfven Waves

Compressional Alfven Waves

Magneto Acoustic Waves

Internal and Magneto Acoustic Gravity Waves

Phase Mixing of Waves

Resonant Absorption of Waves

Nonlinear Aspects

MHD Waves in a Nonuniform Media

Waves at a Magnetic Interface

Surface and Interfacial Waves

Tangential Discontinuity with Inclined Fields and Flows

Two-Mode Structure of Alfven Surface Waves

Magneto Acoustic-Gravity Surface Waves with Flows

Waves in a Magnetic Slab

Negative Energy Waves

Waves in Cylindrical Geometries

Slender Flux Tube Equations

Waves in Untwisted and Twisted Tubes

Applications to Coronal Waves

Nonlinear Aspects

Shock Waves


Discontinuities in Surfaces

Normal Shock Waves

Oblique Shock Waves

Blast Waves: Similarity Solution of Taylor–Sedov

Weak Shock Waves

Waves in a Polytropic Gas

An Application of Shock Waves in the Sun

Shock Waves in Collisionless Plasmas

Shocks in MHD

Nonlinear Studies

Waves in Optics

Optical Phenomena

Nonmonochromatic Fields

Emission of Wave-Trains

Polarization of Plane Monochromatic Waves

Plasma Waves

What Is a Plasma?

Plasma Parameters

Electrostatic Waves in Magnetized Plasma

Waves in a Cold Plasma

Plasma Waves (Warm)-Langmuir Waves

Ion-Acoustic Waves

Waves in Nonhomogeneous Plasmas

Quasilinear Theory for Nonhomogeneous Plasmas

Nonlinear Waves in Plasmas

Fluid and Plasma Instabilities


Stability of Parallel Shear Flows

Taylor–Goldstein Equation

Orr–Sommerfeld Equation

Rayleigh–Taylor (RT) Instability

Kelvin–Helmholtz (KH) Instability

Parametric Instability

Two-Stream Instability

Interchange (Flute) Instability

Sausage Instability

Kink Instability

Ballooning Instability

Appendix A: Typical Tables

Appendix B: Vector Operators



Exercises appear at the end of each chapter.

About the Authors

A. Satya Narayanan is an associate professor at the Indian Institute of Astrophysics. Dr. Narayanan has written two books and numerous research papers. His research interests include solar magnetohydrodynamics (MHD), waves, and oscillations.

Now retired, Swapan K. Saha was a professor at the Indian Institute of Astrophysics. Dr. Saha has written numerous research papers and several books, including High Resolution Imaging: Detectors and Applications. His research interests include observational astronomy, high-resolution imaging, aperture synthesis, adaptive optics, atmospheric science, and image processing.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics