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# Waves

Fundamentals and dynamics
Sanichiro Yoshida

### Description

Waves are everywhere in our daily life. We all experience sound and light with our ears and eyes: we use microwaves to cook, and radio waves are transmitted from, and are received by, our cell phones. These are just some examples of waves that carry energy from point A to B. However, we may not know details of the physics underlying all these waves. It is important to understand the mechanisms that generate wave dynamics for a given system. It is not straightforward to explain how an electromagnetic ﬁeld becomes oscillatory and propagates as a wave. Waves sometimes represent the underlying dynamics of observed phenomena at a fundamental level of physics.

This book is designed to explore these mechanisms by discussing various aspects of wave dynamics from as many perspectives as possible. The target audiences are undergraduate students majoring in engineering science and graduate students majoring in general engineering. Going beyond the typical approach to learning science, this book discusses wave dynamics and related concepts at various levels of mathematics and physics, sometimes touching on profound physics behind them. This book was written to help readers learn wave dynamics on a deep physical level, and develop innovative ideas in their own ﬁelds.

Sanchiro Yoshida is a professor at Southeastern Louisiana University where he teaches optical inferometry and field theory. He received his PhD from Keio University in Tokyo, Japan. His research topics include: Laser Interferometer for Gravitational-wave Observatory (LIGO) and Electronic Speckle Pattern Interferometry (ESPI) for material scientific research.

Preface iii
1 Introduction
1.1 Oscillation and wave
1.2 Oscillation due to centripetal force
1.2.1 Centripetal force
1.2.2 Equation of motion
1.2.3 Oscillation as a solution to equation of motion
1.3 Frequency domain analysis of oscillation
1.3.1 Fourier transform
1.4 Wave
1.4.1 Oscillation to wave

2 Wave equations and solutions
2.1 Wave equation
2.1.1 Transverse waves
2.1.2 Longitudinal waves
2.1.3 Plane wave equation
2.1.4 Decaying wave
2.1.5 Some discussion on phase velocity
2.2 Wave solutions
2.2.1 Plane wave solutions
2.2.2 Paraxial wave
2.2.3 Amplitude and phase of waves
2.2.4 Superposition of waves and Fourier transform

3 Basic properties of waves
3.1 Reﬂection and refraction
3.1.1 Angles of reﬂection and refraction
3.1.2 Coeﬃcient of reﬂection and transmission
3.2 Dispersion
3.2.1 String on an elastic medium
3.2.2 Decaying wave
3.2.3 Light in matter
3.2.4 Transverse wave in beam
3.2.5 Beads on a string
3.3 Interference
3.3.1 Optical interferometry
3.3.2 Acoustic interferometry
3.4 Diﬀraction
3.5 Doppler eﬀect

4 Wave propagation
4.1 Group velocity
4.2 Resonator
4.3 Modulation
4.3.1 Amplitude modulation
4.3.2 Phase modulation
4.3.3 Frequency modulation

### Bibliographic

Paperback ISBN: 9780750328944

Ebook ISBN: 9781681745749

DOI: 10.1088/978-1-6817-4573-2

Publisher: Morgan & Claypool Publishers

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